Apparatus, systems, and methods for non-invasive thermal interrogation

ABSTRACT

Various non-invasive sensors are adapted to be placed on a surface of an object having a volume with an internal region. The internal region of the object has internal properties indicated by corresponding internal parameters and an internal temperature distribution that is a function of the internal parameters and surface thermal signals. Each non-invasive sensor includes a heat flux sensor having one or more heat flux sensor output terminals to provide a measured heat transfer signal for the surface of the object, and a temperature sensor having one or more temperature sensor output terminals to provide a measured temperature signal for the surface of the object. Systems including one or more of the sensors perform non-invasive sensing of the object including accurate and rapid determination of an internal temperature distribution of the internal region of the object as well as one or more other internal properties of the object.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.17/624,207, filed Dec. 30, 2021, which is the U.S. national phase ofInternational Application No. PCT/US2020/040266 filed Jun. 30, 2020which designated the U.S. and claims priority to U.S. Provisional PatentApplication Ser. No. 62/869,208 filed Jul. 1, 2019, the entire contentsof each of which are hereby incorporated by reference.

BACKGROUND

Temperature sensors and other thermal sensing systems are important inmany different technological fields and applications. Of particularimportance are temperature sensors and other thermal sensing systemsthat are non-invasive. The technology in this application is directed tonon-invasive thermal interrogation apparatus, systems, and methods thatprovide improved reliability, accuracy, cost, complexity, size, ease ofmanufacture, ease of use, computational time, processing power required,response time, and applicability across different industries.

Non-Invasive Thermal Interrogation (NITI) provides non-destructivetesting and monitoring using thermal sensing. Non-Invasive ThermalInterrogation (NITI) is conducted using simultaneous combinations ofsurface temperature signals and surface heat transfer (e.g., heat flux)signals. When measured simultaneously on an object or system surface,the surface temperature and surface heat flux signals may be used tonon-invasively determine internal parameters (e.g., thermalconductivity, density, heat capacity, convection coefficient,steady-state thermal resistance, etc.) and internal temperaturedistribution (e.g., an internal temperature profile) of the internalregion of the object or system. The internal temperature distribution ofthe object or system is typically a function of the internal parameters.Depending on the object or system undergoing NITI and/or NITIapplication, the internal parameters may vary. The internal parametersand internal temperature distribution are defined as internal propertiesof the object or system.

Because NITI allows for the non-destructive testing and monitoring of anobject or system whenever thermal signals are present, NITI may beutilized in many diverse applications. In cases where sufficient thermalsignals are not present, they can be generated at the object or systemsurface.

SUMMARY

At least some examples provide a system for non-invasive sensing of anobject having a volume with a surface and an internal region. The systemcomprises a non-invasive sensor including: a heat flux sensor having oneor more heat flux sensor output terminals, and a temperature sensorhaving one or more temperature sensor output terminals. The non-invasivesensor may be placed on or near the surface of the object. The internalregion of the object has internal properties indicated by correspondinginternal parameters and an internal temperature distribution. Controlcircuitry, coupled to the one or more heat flux sensor output terminalsand the one or more temperature sensor output terminals, is adapted to:receive a measured temperature signal from the temperature sensor at oneor more specified times; receive a measured heat flux signal from theheat flux sensor at the one or more specified times; determine a measureof heat transfer leaving or entering the object at the surface based onthe measured heat flux signal at the one or more specified times;determine a value for each of the internal parameters at the one or morespecified times; determine an internal temperature distribution of theinternal region of the object at the one or more specified times basedon the measured temperature signal, the measured heat flux signal, andthe values of the internal parameters; and generate informationindicating the internal temperature distribution of the internal regionof the object at the one or more specified times.

At least some examples provide a system for non-invasive sensing of anobject having a volume with a surface and an internal region. The systemincludes a non-invasive sensor including: a heat flux sensor having oneor more heat flux sensor output terminals, and a temperature sensorhaving one or more temperature sensor output terminals. The non-invasivesensor is adapted to be placed on or near the surface of the object, andthe internal region of the object has internal properties indicated bycorresponding internal parameters and an internal temperaturedistribution. Control circuitry, coupled to the one or more heat fluxsensor output terminals and the one or more temperature sensor outputterminals, is adapted to: receive a measured temperature signal from thetemperature sensor at one or more specified times; receive a measuredheat flux signal from the heat flux sensor at the one or more specifiedtimes; determine estimated values for one or more of the internalparameters at the one or more specified times based on the measuredtemperature signal and the measured heat flux signal; and generateinformation indicating one or more of the estimated values determinedfor the internal parameters at the one or more specified times.

At least some examples provide a system for non-invasive sensing of anobject having a volume with a surface and an internal region. The systemcomprises a first non-invasive, heat flux sensor-temperature sensor pairand a second non-invasive, heat flux sensor-temperature sensor pair.Each of the first and second non-invasive, heat flux sensor-temperaturesensor pairs includes a heat flux sensor having one or more heat fluxsensor output terminals and a temperature sensor having one or moretemperature sensor output terminals. The first and second non-invasive,heat flux sensor-temperature sensor pairs may be placed at differentlocations on or near the surface of the object. The internal region ofthe object has internal properties indicated by corresponding internalparameters and an internal temperature distribution. Control circuitry,coupled to the one or more heat flux sensor output terminals and the oneor more temperature sensor output terminals of each of the first andsecond non-invasive, heat flux sensor-temperature sensor pairs, isconfigured to: receive a first measured temperature signal from thetemperature sensor in the first non-invasive, heat fluxsensor-temperature sensor pair at one or more specified times; receive afirst measured heat flux signal from the heat flux sensor in the firstnon-invasive, heat flux sensor-temperature sensor pair at the one ormore specified times; receive a second measured heat flux signal fromthe heat flux sensor in the second non-invasive, heat fluxsensor-temperature sensor pair at the one or more specified times;determine a value for each of the internal parameters at the one or morespecified times; determine an internal temperature distribution at theone or more specified times based on the measured temperature signalsfrom the temperature sensors in the first and second non-invasive, heatflux sensor-temperature sensor pairs at the one or more specified times,the measured heat flux signals from the heat flux sensors in the firstand second non-invasive, heat flux sensor-temperature sensor pairs atthe one or more specified times, and the values of the internalparameters at the one or more specified times; and generate informationindicating the internal temperature distribution at the one or morespecified times.

At least some examples provide a system for non-invasive sensing of anobject having a volume with a surface and an internal region, comprisinga first non-invasive, heat flux sensor-temperature sensor pair and asecond non-invasive, heat flux sensor-temperature sensor pair. Each ofthe first and second non-invasive, heat flux sensor-temperature sensorpairs includes a heat flux sensor having one or more heat flux sensoroutput terminals and a temperature sensor having one or more temperaturesensor output terminals. The first and second non-invasive, heat fluxsensor-temperature sensor pairs may be placed at different locations onor near the surface of the object. The internal region of the object hasinternal properties indicated by corresponding internal parameters andan internal temperature distribution. Control circuitry, coupled to theone or more heat flux sensor output terminals and the one or moretemperature sensor output terminals of each of the first and secondnon-invasive, heat flux sensor-temperature sensor pairs, is configuredto: receive a first measured temperature signal from the temperaturesensor in the first non-invasive, heat flux sensor-temperature sensorpair at one or more specified times; receive a first measured heat fluxsignal from the heat flux sensor in the first non-invasive, heat fluxsensor-temperature sensor pair at the one or more specified times;receive a second measured temperature signal from the temperature sensorin the second non-invasive, heat flux sensor-temperature sensor pair atthe one or more specified times; receive a second measured heat fluxsignal from the heat flux sensor in the second non-invasive, heat fluxsensor-temperature sensor pair at the one or more specified times;determine an initial value for each of the internal parameters at theone or more specified times; determine one or more internal parametersof the object at the one or more specified times based on the measuredtemperature signals from the temperature sensors in the first and secondnon-invasive, heat flux sensor-temperature sensor pairs at the one ormore specified times and the measured heat flux signals from the heatflux sensors in the first and second non-invasive, heat fluxsensor-temperature sensor pairs at the one or more specified times, andthe values of the internal parameters at the one or more specifiedtimes; and generate information indicating one or more internalparameters of the object at the one or more specified times.

At least some examples provide a non-invasive sensor that may be placedon or near a surface of an object having a volume with an internalregion, where the internal region of the object has internal propertiesindicated by corresponding internal parameters and an internaltemperature distribution. The non-invasive sensor comprises anon-invasive, heat flux sensor-temperature sensor pair that includes aheat flux sensor having one or more heat flux sensor output terminals toprovide a measured heat flux signal for the surface of the object, and atemperature sensor having one or more temperature sensor outputterminals to provide a measured temperature signal for the surface ofthe object. The heat flux sensor and temperature sensor are configuredto be subject to the same thermal conditions.

At least some examples provide a non-invasive sensor that may be placedon or near a surface of an object having a volume with a surface and aninternal region. The non-invasive sensor comprises a first non-invasive,heat flux sensor-temperature sensor pair and a second non-invasive, heatflux sensor-temperature sensor pair. Each of the first and secondnon-invasive, heat flux sensor-temperature sensor pairs includes a heatflux sensor having one or more heat flux sensor output terminals and atemperature sensor having one or more temperature sensor outputterminals. The first and second non-invasive, heat fluxsensor-temperature sensor pairs are adapted to be placed at differentlocations on or near the surface of the object, where the internalregion of the object has internal properties indicated by correspondinginternal parameters and an internal temperature distribution.

Further aspects, features and advantages of the technology presented inthis application will be apparent from the following description ofexamples, which is to be read in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows an example of a heat flux sensor having a thickness t, awidth W, and a length H in accordance with an example heat flux sensorembodiment.

FIG. 2A shows a cross-section of a differential thermopile that includesa thermal resistance layer in accordance with an example embodiment.

FIG. 2B shows a cross-section of a differential thermopile that includesa thermal resistance layer and may be easier to manufacture inaccordance with an example embodiment.

FIG. 3 shows an example where heat flux is imposed across a junction,and the flow of heat is generally restricted to conduction through thecontact spots.

FIG. 4 shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor and a temperature sensor placed on a surfaceof an object with unknown internal properties where a heater (externalthermal device) is placed on the heat flux sensor.

FIG. 5 shows a cross-section of an example CHFT− embodiment thatincludes a heat flux sensor and a temperature sensor placed on a surfaceof an object with unknown internal properties.

FIG. 6A shows a cross-section of an example CHFT− embodiment thatincludes a heat flux sensor, a temperature sensor, and a piece ofinsulation on the heat flux sensor and temperature sensor (i.e., heatflux sensor-temperature sensor pair).

FIG. 6B shows a cross-section of an example CHFT− embodiment thatincludes a heat flux sensor, a temperature sensor, and a piece ofinsulation on the heat flux sensor and temperature sensor (i.e., heatflux sensor-temperature sensor pair) as well as a portion of thesurrounding object area.

FIG. 6C shows a cross-section of an example CHFT− embodiment thatincludes a heat flux sensor, a temperature sensor, and a piece ofinsulation on and surrounding the heat flux sensor and temperaturesensor (i.e., heat flux sensor-temperature sensor pair).

FIG. 7A shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor, a temperature sensor, and an externalthermal device (e.g., a heater).

FIG. 7B shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor, a temperature sensor, and an externalthermal device (e.g., a heater) that provides a thermal event to theheat flux sensor-temperature sensor pair.

FIG. 7C shows an example CHFT+ embodiment which includes a temperaturesensor, a heat flux sensor, a heater, and corresponding outputterminals.

FIG. 7D shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor, a temperature sensor, and an externalthermal device (e.g., a heater), where the temperature sensor is locatedbetween the heat flux sensor and the external thermal device.

FIG. 7E shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor, a temperature sensor, and an externalthermal device (e.g., a heater), where the temperature sensor is locatedwithin the heat flux sensor.

FIG. 7F shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor, a temperature sensor, and an externalthermal device (e.g., a heater), where the heat flux sensor and thetemperature sensor are separated by a substrate.

FIG. 7G shows a cross-section of an example CHFT+ embodiment thatincludes a heat flux sensor, a temperature sensor, and an externalthermal device (e.g., a heater), where the heat flux sensor and thetemperature sensor are separated by a substrate and the temperaturesensor is surrounded by thermally compatible materials.

FIG. 8 is a function block diagram that illustrates an example NITIsystem to perform NITI with a CHFT−.

FIG. 9 is a function block diagram that illustrates an example NITIsystem to perform NITI with a CHFT+.

FIG. 10 is a flowchart outlining non-limiting example proceduresperformed by the control circuitry in an example NITI system thatincludes a NITI sensor for determining one or more internal propertiesof an object, including an internal temperature distribution of theobject at one or more specified times using measured heat flux, measuredtemperature, and determined values of internal parameters of the object.

FIG. 11 is a flow diagram showing example procedures for a parameterestimation scheme performed by the control circuitry in a NITI system.

FIG. 12 shows a cross-section of an example DUO (parallel sensor pairs)CHFT+(with a heater) embodiment placed on a surface of an object withunknown internal properties.

FIG. 13 shows a cross-section of an example DUO (parallel sensor pairs)CHFT− embodiment with different amounts of thermal insulation on eachsensor node.

FIG. 14 shows a cross-section of an example DUO (parallel sensor pairs)CHFT− embodiment with one CHFT− node incorporating thermal insulationwhile the other is exposed.

FIG. 15 shows a cross-section of an example DUO (parallel sensor nodes)CHFT+/− sensing embodiment where one sensor node incorporates a CHFT+and one incorporates a CHFT−.

FIG. 16 shows a cross-section of an example DUO (parallel sensor pairs)CHFT− embodiment where neither sensor node has thermal insulation.

FIG. 17 is a function block diagram that illustrates an example NITIsystem to perform NITI with two non-invasive heat fluxsensor-temperature sensor pairs operating in parallel for determiningone or more internal properties of an object.

FIG. 18A is a flow diagram showing example procedures related to adifferential based data processing method performed by the controlcircuitry.

FIG. 18B is a flow diagram showing example procedures related to adifferential based data processing method performed by the controlcircuitry in steady-state conditions.

FIG. 19A is a flow diagram showing example procedures related to aquotient based data processing method performed by the controlcircuitry.

FIG. 19B is a flow diagram showing example procedures related to aquotient based data processing method performed by the control circuitryin steady-state conditions.

FIG. 20 is a flowchart outlining non-limiting example procedures for anexample DUO NITI embodiment using two non-invasive heat fluxsensor-temperature sensor pairs for determining one or more internalparameters of an object.

FIG. 21 is a flowchart outlining non-limiting example procedures for anexample DUO NITI embodiment using two non-invasive heat fluxsensor-temperature sensor pairs for determining an internal temperaturedistribution of an object.

FIG. 22 shows an example application to blood perfusion (flow) intissue.

FIG. 23 is a graph that shows the parameter estimation scheme's abilityto determine an optimal perfusion (w) value when used with experimentaldata.

FIG. 24 is a graph illustrating an example of matching between acalculated (output) sensor temperature curve and a measured (input)sensor temperature for an example CHFT+ blood perfusion embodiment.

FIG. 25 is a graph illustrating an example of mismatching between acalculated (output) sensor temperature curve and a measured (input)sensor temperature for an example CHFT+ blood perfusion embodiment.

FIG. 26 is a graph illustrating the differing sensitivity of thecalculated (output) sensor temperature curve to internal parameters overtime in the example blood perfusion application.

FIG. 27 is a graph showing results of an example DUO CHFT+ embodimentand an example Periodic CHFT+ embodiment when used to measure perfusionrate of a perfusing pseudo tissue.

FIG. 28 is a graph showing results of an example CHFT+ embodiment(Active Thermometry) when used to measure the core temperature ofperfusing pseudo tissue.

FIG. 29 is a graph showing results of an example CHFT− embodiment(Passive Thermometry) when used to measure the core temperature ofperfusing pseudo tissue.

FIG. 30 is a graph showing results of an example CHFT+ ZHF embodiment(Zero Heat-Flux Thermometry) when used to measure the core temperatureof perfusing pseudo tissue.

FIG. 31 shows another application of the technology to determining oneor more parameters related to fluid flowing in a pipe or other conduit.

FIG. 32 is a graph showing an example correlation developed withexperimental measurements for fluid flow in a copper pipe.

FIG. 33 is a graph showing the parameter estimation scheme's ability indetermining the optimal convection coefficient (h) value when used withexperimental data.

FIG. 34 is a graph showing an example of matching between a calculated(output) sensor temperature curve and a measured (input) sensortemperature for an example CHFT+ fluid flow in copper piping embodiment.

FIG. 35 is a graph showing results of an example CHFT+ embodiment(Active Thermometry) when used to measure the internal temperature offluid flow within a copper pipe.

FIG. 36 is a graph showing results of an example DUO CHFT+/− embodiment(one sensor node with heater and one sensor node without) when used tomeasure the internal temperature of fluid flow within a copper pipe.

FIG. 37 is a graph showing results of an example DUO CHFT+/− embodiment(one sensor node with heater and one sensor node without) when used tomeasure the internal temperature of fluid flow within a CPVC pipe.

DESCRIPTION OF EXAMPLES

Some specific examples will be discussed below. It will be appreciatedthat the invention is not limited to these particular examples.

The following description sets forth example embodiments for purposes ofexplanation and not limitation. But it will be appreciated by thoseskilled in the art that other example embodiments may be employed apartfrom these specific details. In some instances, detailed descriptions ofwell-known methods, interfaces, circuits, and devices are omitted so asnot to obscure the description with unnecessary detail. Individualblocks are shown in some figures. Those skilled in the art willappreciate that the functions of those blocks may be implemented usingindividual hardware circuits, using software programs and data inconjunction with a suitably programmed digital microprocessor or generalpurpose computer, and/or using applications specific integratedcircuitry (ASIC), and/or using one or more digital signal processors(DSPs). Software program instructions and/or data may be stored on anon-transitory, computer-readable storage medium, one or more clouds,one or more servers, and when the instructions are executed by acomputer or other suitable processor control, the computer or processorperforms the functions associated with those instructions.

The term signal is used herein to encompass any signal that transfersenergy and/or information from one position or region to another in anelectrical, electronic, electromagnetic, magnetic, or mechanical (e.g.,ultrasonic signals) form. Signals may be conducted from one position orregion to another by electrical or magnetic conductors, but the termsignals also includes light and other electromagnetic forms of signalsand other signals transferred through non-conductive regions due toelectrical, electronic, electromagnetic, magnetic, or elastic effects.Signals include both analog and digital signals. An analog electricalsignal includes information in the form of a continuously variablephysical quantity, such as voltage. A digital electrical signal includesinformation in the form of discrete values of a physical characteristic,which could also be, for example, voltage.

A component, layer, or other structure is thermally conductive orthermally conducting if it sufficiently conducts thermal energy (e.g.,thermal energy transferred by conduction, radiation, and/or convection)from one position or region to another that operations in the otherposition or region can be affected by the thermal energy. The termsensing means obtaining information from a physical stimulus, andtherefore, sensing includes actions such as detecting, measuring, and soforth. Thermal sensing is sensing of a thermal stimulus such as heat,temperature, or random kinetic energy of molecules, atoms, or smallercomponents of matter. A thermal sensor is an electronic device thatperforms thermal sensing and generates signals related to thermalenergy. If thermal energy includes information, then a thermal sensor orcombinations of thermal sensors that detect the thermal energy may beable to sense the information. Depending on the context, different formsand/or types of thermal energy and related thermal signals, as used inthis application, may be regarded as heat transfer, heat transfersignals, temperature, and temperature signals.

Unless the context indicates otherwise, the terms circuitry and circuitrefer to structures in which one or more electronic components havesufficient electrical connections to operate together or in a relatedmanner. In some instances, an item of circuitry can include more thanone circuit. An item of circuitry that includes a processor maysometimes be separated into hardware and software components; in thiscontext, software refers to stored data that controls operation of theprocessor or that is accessed by the processor while operating, andhardware refers to components that store, transmit, and operate on thedata. Circuitry can be described based on its operation or othercharacteristics. For example, circuitry that performs control operationsis sometimes referred to as control circuitry, and circuitry thatperforms processing operations is sometimes referred to as processingcircuitry.

In general, sensors, processors, and other such items may be included ina system in which they are operated automatically or partiallyautomatically. The term system refers to a combination of two or moreparts or components that can perform an operation together. A system maybe characterized by its operation.

An integrated structure is a structure with electrical components andconnections produced by microfabrication or similar processes. Anintegrated structure may, for example, be on or over a substrate onwhich it was produced or another suitable support structure. Othercomponents could be on the same support structure with an integratedstructure, such as discrete components produced by other types ofprocesses.

Thermal based sensing and monitoring is typically performed with onlytemperature sensors and/or temperature signals. For example, in order todetermine the internal temperature of an object or system, invasivetemperature probes are inserted at a prescribed depth of interest. Anexample uses invasive temperature probes that are inserted inthermowells to measure internal flow temperature within a pipe orconduit. Thermowell placement typically requires complicated procedureswhere the pipe or conduit surface is drilled and/or otherwise penetratedin order to place the thermowell within the internal fluid flow. Atemperature sensor (e.g., thermocouple, resistance temperature device(RTD), thermistor, thermometer, etc.) is then inserted within thethermowell where it is protected from the fluid flow. Due to heatcapacity of the thermowell, the response time of temperature sensorswithin them is slowed. Additionally, because thermowell walls mayconduct heat out of (or into) the pipe or conduit, temperature sensoraccuracy may be negatively impacted. Typically, this approach inmeasuring fluid flow temperature is more accurate than, for example,measuring surface temperature measurements of the pipe or conduit.However, due to the invasive nature of such technology, a number ofdesign considerations typically take place before their use. Thesedesign considerations can be complicated and costly for manyapplications. For example, the material and/or design characteristics ofthe thermowell may differ based on application and need to adhere toextensive standards (e.g., American Society for Testing and Materials(ASTM) standards). Furthermore, the invasive nature of thermowellsresults in complicated long term maintenance, e.g., due to corrosionand/or prolonged exposure to high energy fluid flow which can causestructural stress and vibrations.

Another thermal based sensing example of where invasive probes are usedfor object and/or system internal temperature measurement is core bodytemperature measurement. For example, in healthcare, the current methodsutilized and accepted as accurate methods of real-time core bodytemperature measurement are, for example, esophageal, rectal, andpulmonary artery based temperature measurements. All of these methodsutilize invasive and often uncomfortable probes that are placed atdifferent locations within the body. Because of their invasive nature,such methods can lead to infection and/or other complications. Theinvasive nature of such methods also limits the scope of where and whenmeasurements can be made. For example, invasive probes are rarely usedunless the patients have undergone anesthesia or other similarprocedures. Invasive probes are also not suitable for wearabletechnologies or devices.

Given the limitations of invasive internal temperature measurementtechnologies, an alternative approach may be to make internaltemperature measurements of an object or system based on surface and/orother external temperature readings (e.g., ambient temperature). Thisapproach, however, typically results in inaccurate measurements and mayrequire complex hardware and software systems in an attempt to determineinternal temperature measurements based on such non-invasive temperaturemeasurements. In some embodiments, multiple temperature sensors may beused on or near an object or system surface and/or internally within adevice that is placed on or near the surface of the object or system. Inaddition, one or more thermally calibrated components (e.g., insulationpieces, precise temperature sensors, etc.) may be required. This furtherresults in complicated and/or complex measurement systems. Otherembodiments may include one or more control systems, one or moreheaters, one or more coolers, and/or multiple temperature sensors. Theseembodiments may be, for example, designed to create and determine a zeroheat-flux environment for internal temperature measurement. Suchnon-invasive approaches are typically slow and inaccurate, especially inchanging or extreme thermal conditions. Furthermore, in some cases, foraccurate internal temperature measurements, sensor and/or deviceplacement may be limited to specific areas on an object or systemsurface. For example, with regard to core body temperature measurement,sensor and/or device placement may be limited to certain auxiliarylocations on the body (e.g., armpit or forehead). Additionally, due tohardware complexity, embodiments may be associated with large formfactors, resulting in an inconvenience for many applications. Forexample, with regard to core body temperature measurement, large formfactors are impractical for wearable applications. With regard tonon-invasive internal pipe or conduit temperature measurement, largeform factors may prevent sensor and/or device mounting in certainlocations, e.g., in between a pipe surface and surrounding thermalinsulation. Finally, the complexity of such systems may result inmanufacturing difficulty as well as increased manufacturing costs.

Other thermal based sensing applications may use temperature basedsignals to determine internal fluid flow via thermal anemometry. Thisapproach requires internal probing in order to make measurements offluid flow that correspond to measured temperature signals viaestablished correlations. To the contrary, thermal dispersion flowmeters are non-invasive systems that use temperature sensors on thesurface of a pipe or conduit in between which a heater provides thermalenergy into the pipe/conduit surface. The temperature difference betweenthe temperature sensors placed before and after the heating element iscorrelated to internal fluid flowrate. However, thermal dispersion flowmeters do not function properly with pipes made of thermally insulatingmaterials. Furthermore, they are susceptible to inaccuracies when usedin differing conditions because the specific amount of thermal energy(i.e., heat transfer) entering the pipe or conduit via the heater isunknown and can only be estimated with underlying assumptions. Thus,thermal dispersion flow meters are typically calibrated for specificconditions and use cases.

Other thermal based technologies may be used to predict (e.g.,analytically determine) object or system surface heat transfer (e.g.,heat flux) using surface and/or internal temperature measurements. Suchtechniques may be further used to determine internal properties of anobject or system based on the predicted surface heat transfer (e.g.,heat flux) and surface or internal temperature signals. However, thesetechniques may have a number of limitations such as poor accuracy, lowresolution, prolonged processing time, and noise amplification due to amathematical integration required when determining heat transfer (e.g.,heat flux) from measured temperature signals.

For example, determined surface heat transfer (e.g., heat flux) of anobject or system may be compared with measured surface heat transfer(e.g., via a heat flux sensor) in order to determine internal propertiesof the object or system. Again, due to the limitations of heat transfer(e.g., heat flux) prediction based on temperature measurements, thevalues determined via such techniques for internal properties of anobject or system may be inaccurate and impractical for application.Furthermore, when using such techniques, there may be a mismatch betweenthe measured temperature (e.g., surface temperature), from which surfaceheat transfer is determined, and the measured heat transfer (e.g.,surface heat flux) of an object or system. For example, a mismatch mayoccur when the heat transfer (e.g., heat flux) measured at the object orsystem surface, e.g., via a heat flux sensor, is not the same as theheat transfer (e.g., heat flux) occurring at the location of the surfacetemperature sensor. This can be caused by, for example, a surfacetemperature sensor that is located in proximity to a heat flux sensorwhere it is not subject to the same thermal (e.g., heat transfer and/ortemperature) conditions experienced by the heat flux sensor. In otherexamples, a temperature sensor may be located on or near a heat fluxsensor but in a location outside of the heat flux sensor sensing area,which may also result in a mismatch of measurements. Similar issues mayarise when using a temperature sensor that, for example, is located onor near a heat flux sensor sensing area but causes inadequate contactbetween the heat flux sensor and object/system surfaces as a result of,for example, its design (e.g., thickness) and/or materials. In thisexample, the mismatch occurs because the measured temperature is not anaccurate representation of the surface temperature and/or the measuredheat transfer is not realistic of what is occurring at the object/systemsurface and/or experienced by the temperature sensor. In other examples,the materials used to construct the heat flux sensor and temperaturesensor and/or their surroundings may be sufficiently different (e.g.,different thermal resistance values) and cause a non-uniform response touniform thermal conditions. This may also result in a mismatch betweenthe heat flux sensor and temperature sensor outputs.

In another example, a thin-film thermocouple, which is an example thintemperature sensor, may be located on a heat flux sensor sensing areawhere adequate contact is established between the heat flux sensor andobject/system surfaces. In this case, although the thin-filmthermocouple temperature sensor does not create any of the exampleissues described above (e.g., inadequate contact due to thickness) andis subject to the same thermal (e.g., heat transfer and/or temperature)conditions as the heat flux sensor, it may experience thermal shuntingwhere the measured temperature is inaccurate due to thermal energy beingconducted to or from (i.e., leaving or entering) the thermocouplejunction via the thermocouple materials and/or output terminals (e.g.,thermocouple leads). In such cases, the measured temperature may belower or greater than the actual temperature experienced at or near theheat flux sensor sensing area. All of these non-limiting and exampleconditions are potential issues for accurate determination of an objector system internal properties when using thermal based sensingtechnologies.

A problem with using heat transfer (e.g., heat flux) measurements inthermal based sensing technologies is inefficiency. Heat transfer isconventionally understood and explained as a consequence of temperaturegradients. This conventional approach may lead to inefficient andinaccurate heat transfer (e.g., heat flux) measurement techniques aswell as general confusion between the differences of heat transfer(e.g., heat flux) and temperature. For example, one way to measure heattransfer may use one or more temperature sensors, e.g., thermocouples,RTDs, negative or positive temperature coefficient (NTC) sensors,thermistors, etc. on either side of some sort of insulating material(i.e., thermal resistance layer) to create a layered heat flux gage, atype of one-dimensional planar (i.e., flat) gage. In this examplemethod, a determination (e.g., average) of absolute temperature oneither side of the insulating material is measured, and the differencebetween them is used to determine the amount of heat transfer occurringthrough the insulating material with a calibrated or otherwisedetermined thermal resistance value. In another example approach, athermocouple may be placed on either side (e.g., top and bottom) of acalibrated insulating material (i.e., thermal resistance layer), forminga thermocouple pair. The thermocouple pair may be arranged so that, whenconnected in series, the output of the thermocouple pair is adifferential voltage that is indicative (e.g., proportional) to thetemperature difference across the thermal resistance layer and to theheat transfer (e.g., heat flux) occurring through the thermal resistancelayer. These example approaches may result in slow, inaccurate, highcost, and large heat flux device(s) (i.e., heat flux channel(s)) thatmay require multiple calibrations and may be difficult to manufacture.

Another shortfall in thermal based sensing techniques is failure todetermine or otherwise account for thermal contact resistance. Thisleads to erroneous surface temperature measurement which may influencethe accuracy of thermal based sensing and monitoring. However, modelingand/or determination of thermal contact resistance when performingthermal based sensing may be difficult and unclear. This is in part dueto the complexity and inaccuracies associated with determining thermalcontact resistance using only temperature signals and/or methods thatpredict heat transfer based on temperature signals.

The technology described in this application solves these technicalproblems and provides the following example technical benefits. Mostimportantly, in addition to a measure of surface temperature, thetechnology described in this application provides a measure of the heattransfer (e.g., heat flux) entering or leaving an object and/or systemsurface as a part of a thermal based sensing and/or monitoring routine(i.e., technique). This measure of heat transfer (e.g., heat flux) isused as a direct input and/or a boundary condition in one or morethermal mathematical model(s) that may differ for differentapplications. The measure of heat transfer (e.g., heat flux) as an inputand/or direct boundary condition, allows for accurate and robust thermalsensing and monitoring (i.e., interrogation) techniques.

The technology performs the measure of heat transfer (e.g., heat flux)via one or more heat flux sensor(s). For the purpose of thisapplication, the term heat flux sensor refers to a sensor designed tomeasure heat transfer (e.g., heat flux) using differential voltageoutput signals that are a consequence of the heat transfer (i.e.,thermal energy) flowing through the sensor. A non-limiting example of ameasure of heat transfer is heat flux which is defined as the amount ofthermal energy entering or leaving a surface per unit of area per unitof time and can be measured in SI units of W/m². A heat flux sensortypically has a calibration constant (i.e., sensitivity value) thatdirectly relates the heat flux sensor differential voltage outputsignals to the heat transfer (e.g., heat flux) occurring through it. Acalibration constant may vary with sensor operating temperature, theeffects of which can be accounted for via a determined calibration curvethat specifies a calibration constant based on sensor operatingtemperature. As pertains to this application, it is important to notethe distinctions between a heat flux sensor and a heat flux device, aheat flux channel, etc. A heat flux sensor is typically thin and has afast response time as a result of its design. This provides examplebenefits including increased accuracy, a smaller form factor, and robustmeasurement capability unrealized by other heat transfer measurementtechnologies.

Additionally, the technology described in this application ensures,regardless of the proximity of the temperature sensor to the heat fluxsensor (e.g., next to, on, or near the heat flux sensor sensing area,etc.), that a mismatch does not exist between the measured temperature(e.g., surface temperature) and the measured heat transfer (e.g.,surface heat flux) of an object or system (e.g., the heat flux sensorand temperature sensor are subject to the same thermal conditions). Forexample, when possible, the temperature sensor may be located on or nearthe heat flux sensor sensing area while maintaining adequate contactbetween the heat flux sensor and object/system surfaces and, ifapplicable, designing for possible effects related to thermal shuntingand/or thermal homogeneity of materials used for construction. In otherexample embodiments, the temperature sensor may be located on or near(e.g., adjacent to) the heat flux sensor and/or the heat flux sensorsensing area and may be surrounded by and/or in contact with materialsthat ensure the same thermal (e.g., heat transfer and/or temperature)conditions between the heat flux sensor and temperature sensor.

Another major benefit of the technology in this application is theability to easily and quickly determine thermal contact resistancebetween a temperature sensor and object or system surface. This improvesthe accuracy and validity of thermal sensing and monitoring, especiallyin example applications where the effects of thermal contact resistanceare not negligible and/or unpredictable.

Another major benefit of the technology in this application isnon-invasiveness and simplicity of use. For example, extensive designconsiderations or precautions required for invasive technologies are notneeded. Furthermore, the technology is not restricted to applicationswhere invasiveness is permissible.

Further benefits of the technology in this application include minimalprocessing time and reduced processing power required. This benefit isin part attributed to the use of a heat flux boundary condition as wellas incorporating fast and refined methods of determining thermal contactresistance. Reduced calibration needs for sensors designed for heattransfer (e.g., heat flux) measurement is another benefit. For example,the technology in this application typically only requires onecalibration constant (i.e., sensitivity value) for heat transfermeasurement via a heat flux sensor.

The technology in this application is based on the simultaneous use ofheat flux and temperature sensors to non-invasively determine one ormore internal properties of an object and/or system. Object(s) and/orsystem(s) are not limited to solid objects but also include, forexample, fluid (e.g., water, air, etc.) or other material(s), e.g.,metallurgic powder, epoxies, carbon fiber composite materials, etc. Forsimplicity, the term object as used in this application includes asystem. For example, a pipe with fluid flowing inside is an object. Theterm Non-Invasive Thermal Interrogation (NITI) is used herein to referto sensor technology based on simultaneous combinations of surface heatflux and surface temperature measurements. When placed on an object, anNITI sensor measures one or more simultaneous combinations of surfaceheat transfer (e.g., heat flux) and surface temperature signals that areconverted to digital form and processed to determine one or moreinternal properties of the object. For a given measurement, the termsimultaneous combination as used in this application refers to one ormore surface heat transfer (e.g., heat flux) and surface temperaturesignals measured within a range of time (i.e., within a specified amountof time). A range of time may include a single time (i.e., a specifiedtime). For simplicity, the term specified time as used in thisapplication is defined to include a range of time (i.e., within aspecified amount of time) as well as a single time.

Non-limiting, example applications of the NITI technology include butare not limited to: internal temperature distribution measurement of anobject (e.g., mammal, non-mammal, meat, pipe/conduit, power transformer,lumber/timber, wall, machine, battery, etc.), internal parametermeasurement of an object (e.g., mammal, non-mammal, meat, pipe/conduit,power transformer, lumber/timber, wall, machine, battery, etc.), bloodperfusion (flow) measurement of tissue, tissue ulcer prevention and/ormonitoring, hemorrhage detection and/or monitoring, concussion detectionand/or monitoring, hydration measurement of tissue, metabolic heatgeneration measurement, athlete performance monitoring, calorieexpenditure measurement, sleep monitoring, circadian rhythm monitoring,ovulation prediction and/or detection of mammals, heatstroke monitoringand/or prevention, sickle cell anemia detection and/or monitoring,anemia detection and/or monitoring, cardiovascular heath, skin flapand/or graft monitoring, disease/illness prediction, monitoring, and/ordetection (e.g., Alzheimer's, Parkinson's, cancer, etc.), flow ratemeasurement in pipes and/or conduits, energy measurement in pipes and/orconduits, pipe/conduit freezing prevention, pipe/conduit defrosting,HVAC frost/defrost detection, HVAC system monitoring, HVAC refrigerantlevel monitoring, leak detection (e.g., pipe/conduit water leak, HVACrefrigerant leak, etc.), hot water heater monitoring, heat exchangermonitoring, corrosion detection and/or measurement (e.g., pipe/conduitcorrosion, etc.), fouling detection and/or measurement (e.g.,pipe/conduit fouling, etc.), flow level detection, presence and/ormotion detection, semiconductor hardware monitoring, heat sinkperformance monitoring, thermal interface material monitoring, thermalresistance measurement, building insulation measurement, density, heatcapacity, volumetric heat capacity, thermal conductivity, thermalinertia, thermal effusivity, thermal diffusivity, etc. of object(s)and/or material(s) (e.g., metallurgic powder, epoxies, carbon fibercomposite materials, etc.) measurement, hydration/water contentmeasurement, convective heat transfer coefficient measurement, advectionheat transfer coefficient measurement, heat treatment, thermalsanitation, thermal processing, thermal comfort, thermal performance ofbuildings, precision agriculture, smart farms, food processing, freezingof objects, thawing of objects, metallurgic processing, 3D printing,quality control of objects, smart buildings, efficiency monitoring,object overheating prevention, object (e.g., machine, gearbox,compressor, fan, electro-mechanical system, etc.) failure detectionand/or prediction/prevention, advanced temperature control, batteryperformance monitoring (e.g., lithium-ion battery state of healthovertime, etc.), battery calorimetry, internet of things (IoT), wearablesensors, predictive analytics, prescriptive analytics, descriptiveanalytics, artificial intelligence, and research and development.

The term internal temperature distribution of the internal region of anobject (i.e., internal temperature distribution) as used in thisapplication includes a single temperature at a specific depth in theobject at one or more specified times, multiple temperatures as afunction of depth in the object at the one or more specified times, asingle average temperature at a specific depth in the object at one ormore specified times, multiple average temperatures as a function ofdepth in the object at the one or more specified times, a single highestor lowest temperature in the object at one or more specified times,multiple highest or lowest temperatures in the object at the one or morespecified times, a single highest or lowest average temperature in theobject at one or more specified times, or multiple highest or lowestaverage temperatures in the object at the one or more specified times.Furthermore, the internal temperature distribution of the internalregion of the object is defined to include measures of object surfacetemperature. For example, the internal temperature distribution may beevaluated at the object surface (i.e., depth (x) of 0) at one or morespecified times.

The term internal parameters of the internal region of an object (i.e.,internal parameters) as used in this application includes one or morethermal, physical, mechanical, etc. characteristics of the object. Forexample, internal parameters of the object may include the thermalconductivity of the object, the density of the object, the thermal heatcapacitance of the object, the volumetric heat capacity of the object,the thermal diffusivity of the object, the thermal inertia of theobject, the thermal effusivity of the object, the steady-state thermalresistance of the object, the internal or external convectioncoefficient of the object, the internal or external advectioncoefficient of the object, the thickness of the object, the volume ofthe object, the mass of the object, the cross-sectional area of theobject, the porosity of the object, the state of the object (e.g.,liquid, solid, gas, etc.), the depth of interest from the surface of theobject, etc. Some internal parameters may be based on a combination ofinternal parameters (e.g., a quotient and/or product of two or moreinternal parameters). Furthermore, not all internal parameters of anobject may be utilized and/or necessary for an NITI embodiment and/orapplication. For simplicity, the term internal parameters as used inthis application includes one or more internal parameters that arenecessary and/or desired for the NITI embodiment being performed for theobject (i.e., corresponding internal parameters).

NITI Sensor Example Embodiments

Example sensor embodiments for NITI (i.e., NITI sensors) include one ormore heat flux sensors and one or more temperature sensors. A heat fluxsensor and a temperature sensor that are subject to the same thermal(e.g., heat transfer and/or temperature) conditions and makesimultaneous measurements at one or more specified times are referred toas a heat flux sensor-temperature sensor pair (i.e., sensor pair). ANITI sensor may also include an external thermal device that is usedwith a control circuitry intended for NITI.

In other example sensor embodiments, an optional external thermal devicecreates a thermal energy source on one side of a NITI sensor thattravels through the NITI sensor and into an object for whichmeasurements are being made. In other example embodiments, an optionalexternal thermal device creates a thermal energy sink (i.e., heatsink)on one side of a NITI sensor that causes heat transfer from an object,for which measurements are being made, through the NITI sensor, and intothe heatsink. An external thermal device may be a heater and/or cooler(e.g., a Peltier device) that is used with a control circuitry intendedfor NITI to create a thermal event (heating and/or cooling) so thatdiffering simultaneous combinations of heat transfer (e.g., heat flux)and temperature signals can be generated at an object surface, acquired(e.g., measured), and processed. An external thermal device may operatein any manner (steady, periodic, cycled, etc.). In some exampleembodiments, an external thermal device may be used to provide aperiodic (e.g., sinusoidal) temperature and/or heat flux condition atthe object surface over time. Further example embodiments use phaseangle determination techniques with one of more of the NITI techniquesdescribed to determine one or more internal properties of the object.

Typically, the external thermal device is adapted to provide the thermalevent to an area encompassing the entirety of the heat fluxsensor-temperature sensor pair where, at a minimum, the entire heat fluxsensor sensing area is subject to the thermal event. In other exampleembodiments, the external thermal device may be adapted to provide thethermal event to an area encompassing the entirety of the heat fluxsensor-temperature sensor pair as well as object surface areassurrounding the heat flux sensor-temperature sensor pair. In otherexample embodiments, an external thermal device may provide a thermalevent to multiple heat flux sensor-temperature sensor pairs. In otherexample embodiments, for example, when the object undergoinginterrogation has a non-planar (e.g., curved) surface, an externalthermal device may be designed provide a thermal event to the areaincluding a heat flux sensor-temperature sensor pair and not thesurrounding object surface,

In other example sensor embodiments, an external thermal device may beused with a control circuitry intended for NITI to eliminate the heattransfer occurring between the object and NITI sensor surfaces. Forexample, an external thermal device (e.g., heater) could apply or removeheat (i.e., thermal energy) at the object surface and create a “zeroheat-flux environment” between the contacting object and NITI sensorsurfaces. In a zero heat-flux environment, the heat flux sensorcomponent of the NITI sensor, outputs and maintains a minimal voltage(e.g., “0”) and, when in steady-state conditions, the correspondingsurface temperature measured by the NITI sensor at the object surface isindicative of the internal temperature distribution of the internalregion of the object.

With regard to example NITI sensor and/or system embodiments describedbelow, CHFT+/− refers to Combined Heat Flux and Temperature Sensor(i.e., heat flux sensor-temperature sensor pair) and the + or −indicates use of an external thermal device (e.g., heater, Peltierdevice, etc.) that is used with a control circuitry intended for NITI ornot, respectively. DUO NITI refers to NITI sensor and/or systemembodiments with multiple (e.g., two) NITI sensors (e.g., CHFT+ orCHFT−) operating in parallel. DUO NITI example embodiments may, forexample, use differential and/or quotient based data processing methodsto simplify and make more robust NITI measurements. Furthermore, DUOCHFT+ refers to DUO NITI example embodiments that only utilize two ormore parallel CHFT+ embodiments. Similarly, DUO CHFT− refers to DUO NITIexample embodiments that only utilize two or more parallel CHFT−embodiments. DUO CHFT+/− refers to DUO NITI example embodiments thatutilize at least one CHFT+ example embodiment and at least one CHFT−example embodiment operating in parallel. As related to thisapplication, CHFT+, CHFT−, DUO CHFT+/−, DUO CHFT+, and DUO CHFT− arenon-limiting examples of NITI sensor embodiments that may be utilized indifferent NITI systems, some of which are described below.

Although heat flux device(s), heat flux channel(s), etc. may be used forNITI, heat flux sensor(s) are preferred for reasons described prior. Allkinds of heat flux sensor(s) (i.e., heat flux gage(s), heat fluxgauge(s), heat flux transducer(s), heat flux meter(s), heat flowmeter(s), heat flow gage(s), heat flow gauge(s), etc.) that aremanufactured using a variety of methods and technologies (e.g.,thin-film technologies, thick-film technologies, thermopiletechnologies, differential thermopile technologies, thermoelectrictechnologies, Seebeck effect technologies, transverse Seebeck effecttechnologies, butt-weld technologies, Microelectromechanical System(MEMS) based technologies, Nanoelectromechanical System (NEMS) basedtechnologies, Complementary metal-oxide-semiconductor (CMOS) basedtechnologies, additive manufacturing technologies, screen printingtechnologies, ink-jet technologies, textile sensor technologies,wire-wound technologies, RTD based technologies, NTC based technologies,thermistor based technologies, semi-conductor based technologies, etc.)may be used for NITI. In some example embodiments, the one or more heatflux sensors are based on differential thermopile technology asdescribed by ASTM standard E2684 and further discussed in ASTM standardE2683. A differential thermopile is a type of passive electronictransducer that converts thermal energy into electrical energy (e.g.,voltage and/or current). A differential thermopile is typically composedof several thermocouples connected in series or, less commonly, inparallel. Typically, the thermocouples (i.e., thermocouple junctions)are located on either side of one or more materials (i.e., thermalresistance layer). The individual thermocouples (i.e., thermocouplejunctions) measure the temperature differential from their junctionpoint to the point in which the thermocouple voltage output is measured.When in series, the voltage output of two thermocouples on either sideof a thermal resistance layer (i.e., a differential thermocouple pair orthermocouple pair) is typically a differential voltage that is related(e.g., proportional) to the temperature difference across (e.g.,through) the thermal resistance layer and to the heat transfer (e.g.,heat flux) occurring through the thermal resistance layer. Adding morethermocouple pairs in series increases the magnitude of the differentialvoltage output, consequently resulting in higher heat flux sensorsensitivity. The differential voltage output is also affected by thethermocouple (i.e., thermoelectric) materials used. Hence, for a giventemperature difference across a thermal resistance layer, somethermocouple materials may result in a higher differential voltageoutput than others. Thus, thermocouple material selection also impactsheat flux sensor sensitivity. Likewise, the materials and/or thicknessused for the thermal resistance layer may affect heat flux sensorsensitivity as well as heat flux sensor response time. Differentialthermopiles can be constructed with a single thermocouple pair, composedof at least two thermocouple junctions, or multiple thermocouple pairs.Differential thermopiles do not measure absolute temperature, butinstead generate a differential voltage output indicative of (e.g.,proportional to) a local temperature difference or temperature gradient.This temperature gradient, as previously mentioned, is a consequence ofthe heat transfer (e.g., heat flux) occurring through the differentialthermopile and/or thermal resistance layer and, thus, indicates ameasure of the heat transfer (e.g., heat flux) occurring through thedifferential thermopile and/or thermal resistance layer.

One example differential thermopile for heat transfer measurements isconstructed using thin-film materials and polyimide (i.e., thermalresistance layer) to create a thin heat flux sensor with accuratereadings and fast response time («1 second). Another example may bedifferential thermopiles constructed via one or more electricallyconductive through holes (i.e., VIAs) in a thermal resistance layer.Other examples could include devices that are based on differentialthermopile technology but are designed to convert thermal energy toelectrical power via, for example, thermal energy harvesting (e.g.,Thermoelectric Generators (TEGs)). In addition to thermal energyharvesting, these devices can be utilized as heat flux sensors giventhey can output a differential voltage indicative of (e.g., proportionalto) the heat transfer (i.e., thermal energy) occurring through thedevice. However, due to different design criteria, current TEGtechnology is often expensive and have large form factor when comparedto differential thermopiles that are designed for heat flux sensorapplications. Thus, using such devices can result in difficulty of useand/or inaccuracy of heat transfer (e.g., heat flux) measurements aswell as slow response time. Another example is textile based heat fluxsensor(s) where a differential thermopile is constructed within fabricor other materials designed to be worn or otherwise in contact with orin proximity to, for example, the human body.

For simplicity, the measure of heat transfer measured by heat fluxsensor(s) as used in this application is heat flux with units of W/m².This is an example and non-limiting measure of heat transfer that may beused for NITI and/or associated topics (e.g., heat flux sensor design,thermal contact resistance effects, data processing methods, etc.).

FIG. 1 shows an example of a heat flux sensor based on differentialthermopile technology having a thickness t, a width W, and a length H. Asensing area is defined by a width A and a length B, and sensor outputsinclude heat flux output voltage leads (i.e., output leads).

FIG. 2A shows a cross-section of an example differential thermopile thatincludes a thermal resistance layer where k is the thermal conductivityof the thermal resistance layer, T₁ is a hot temperature junction, T₂ isa cold temperature junction, ΔT is the temperature difference between T₁and T₂ and equivalent to the temperature difference across the thermalresistance layer, and ΔV is the differential voltage output by thethermocouple pairs connected in series and is directly indicative of(e.g., proportional to) ΔT, which is a consequence of q″, the heat fluxoccurring through the thermal resistance layer. The greater the numberof thermocouple pairs, the greater the heat flux sensor sensitivity(greater ΔV for a given amount of q″). In this example, each temperaturejunction is formed by connecting two dissimilar thermoelectric materials(e.g., M1 and M2) in series through the thermal resistance layer.Dissimilar thermoelectric materials may include materials that havedifferent Seebeck coefficients in order to generate a thermoelectricvoltage (e.g., copper and constantan, copper and nickel, copper andsilver, antimony and bismuth telluride, positively doped materials andnegatively doped materials, p-type semiconductor materials and n-typesemiconductor materials, etc.)

FIG. 2B shows another example differential thermopile that includes twodissimilar thermoelectric materials (i.e., M1 and M2) as well as anelectrical conductor (M3). In this example embodiment, M3 is used toconnect M1 and M2 in series through the thermal resistance layer. Thisconfiguration of the example differential thermopile has examplebenefits including lower cost of manufacture, higher sensitivity,greater design freedom, etc. and may be realized using one or moremanufacturing technologies (e.g., MEMS based technologies, NEMS basedtechnologies, CMOS based technologies, additive based technologies,etc.). In other example embodiments, manufacturing may further besimplified where M3 is designed to be the same material as M1 or M2.

When a thermocouple junction is formed by pressing two similar ordissimilar metallic materials together or when a temperature sensor isput in contact with an object surface, only a small fraction of thenominal surface area is actually in contact because of the non-flatnessand roughness of the contacting surfaces. If a heat flux is imposedacross the junction and/or the surfaces in contact, the flow of heat(i.e., thermal energy) is generally restricted to conduction through thecontact spots. See the example shown in FIG. 3 . The limited number andsize of the contact spots results in an actual contact area which issignificantly smaller than the apparent contact area. This limitedcontact area and the presence of gaps causes a thermal resistancereferred to as contact resistance or thermal contact resistance(R_(C)″).

The presence of thermal contact resistance (R_(C)″) affects the qualityof temperature measurement. Specifically, the presence of thermalcontact resistance (R_(C)″) between a temperature sensor of, forexample, an example NITI embodiment and object surface causes inaccuratetemperature readings. In other words, the actual surface temperature ofan object differs from what is measured by a temperature sensor evenwhen adequate contact and thermal shunting design is achieved via, forexample, thin-film thermocouple technology. This inaccuracy is relatedto the amount of thermal contact resistance (R_(C)″) present (typicallyconstant) and the heat flux occurring through it at a specified time.This relationship is expressed below mathematically:

T _(Surface)(t)=T _(Sensor)(t)−q _(Sensor)″(t)×R _(C)″  [1]

where heat flux is defined to be positive when entering the object andwhere:t is a specified time, q_(Sensor)″(t) is the measured heat flux at thespecified time, T_(Sensor)(t) is the sensor measured surface temperature(i.e., measured sensor temperature, measured temperature) at thespecified time, and T_(Surface)(t) is the actual surface temperature atthe specified time. As pertains to this application, unless the contextindicates otherwise, the thermal contact resistance (R_(C)″) between atemperature sensor of an example NITI sensor embodiment and objectsurface may be referred to as the thermal contact resistance between theNITI sensor and the object surfaces.

FIG. 4 shows an example CHFT+ embodiment that includes a heat fluxsensor and a temperature sensor placed on a surface of an object withunknown internal properties relating to an internal region of the objectand where a heater (i.e., external thermal device) is placed on the heatflux sensor. In this example, a heat flux sensor contacts with atemperature sensor which contacts with a surface of the object. Again,the limited contact area between the temperature sensor and objectsurface causes a thermal resistance between the temperature sensor andthe object surface temperature and is shown as a thermal contactresistance (R_(C)″). Additionally, layers (e.g., as a result ofprotective layers, adhesives, etc.) on the temperature sensor can impact(e.g., increase) the amount of thermal contact resistance (R_(C)″)present. Heat flux (q″) is shown as a vector pointing into the objectand is defined to be positive in that direction. Thus, as indicated inEquation [1], the object's actual surface temperature (T_(Surface)(t))is determined using the measured temperature from the temperature sensor(T_(Sensor)(t)), the measured heat flux from the heat flux sensor(q_(Sensor)″(t)), and the thermal contact resistance (R_(C)″). In someexample embodiments, an effort may be made to minimize the thermalcontact resistance (R_(C)″) in order to assume a value of “0” inEquation [1]. This may be done, for example, by using thermallyconductive adhesives in between the contacting surfaces.

In other example embodiments, to obtain an accurate actual surfacetemperature measurement (T_(Surface)(t)), an estimated value for thethermal contact resistance (R_(C)″) may need to be determined (e.g.,measured). In some cases, the estimated thermal contact resistance(R_(C)″) (i.e., thermal contact resistance (R_(C)″)) value may bedetermined to be negligible or zero. In other cases, the estimatedthermal contact resistance (R_(C)″) value may be determined usingpredetermined specifications from, for example, a manufacturespecification for an adhesive tape used to mount an NITI sensor.

Example embodiments are capable of making accurate NITI measurements ofan object whether conducted in steady-state or transient environments.The example embodiments utilize heat flux boundary conditions in theirrespective thermal mathematical models (heat flux is an input) which aremore robust and accurate than temperature based boundary conditions.Example outputs include accurate values for internal properties of anobject such as an internal temperature distribution of the internalregion of the object and/or one or more internal parameters of theobject.

Referring to FIG. 5 , an example CHFT− embodiment includes a heat fluxsensor and a temperature sensor placed on a surface of an object withunknown internal properties. One example application is in situationswhere there is some form of an external thermal event occurring, e.g., aCHFT− is placed on an engine where the external thermal event is theheat produced and emitted by the engine. Another application is wherethe CHFT− is placed on the body of a human or other animal, e.g., anathlete exercising. In this latter example, the combination of body heatdissipation and airflow moving over the CHFT− corresponds to an externalthermal event. Other external thermal events could be sourced from aheat lamp, a fan, a heat sink, solar radiation, contact with otherobjects (e.g., metal plates), etc. that are not used with a controlcircuitry intended for NITI (i.e., uncontrolled external thermal event).

To limit heat flux noise and sporadic signals from registering as aresult of, for example, small environmental changes and/or otherexternal stimuli, a piece of thermal insulation (i.e., layer of thermalinsulation or insulation piece) may be placed on top of the CHFT− asshown in FIG. 6A. This piece of insulation acts as a filter and onlyallows substantive heat flux and temperature signals to be detected bythe CHFT−. Furthermore, the thermal insulation piece can be used tocontrol (i.e., limit, increase, etc.) the amount of heat flux occurringthrough the CHFT−. The thickness, material, form factor, and size of theinsulation piece is dependent on the application the CHFT− is being usedfor among other factors. In some example embodiments, thermal insulationmay be embedded within a substrate or material on which the heat fluxsensor and/or temperature sensor is mounted. For example, air gaps orother areas with low thermal conductivity may be designed within aprinted circuit board (e.g., rigid and/or flex material) that is used toarrange and connect electrically connect to the heat flux sensor and/ortemperature sensor.

FIG. 6A shows an example where the thermal insulation piece is adaptedto cover the entirety of the heat flux sensor-temperature sensor pair.In other example embodiments, as illustrated in FIG. 6B, the insulationpiece may also overlap object surface areas surrounding the heat fluxsensor-temperature sensor pair. In some example embodiments, such asillustrated in FIG. 6C, the thermal insulation piece or additionalthermal insulation may be specified to surround the heat flux sensorand/or temperature sensor to minimize thermal loss. In some exampleembodiments thermal insulation materials could include metals or otherthermally conductive materials designed to enhance and increase theamount of heat flux occurring through the CHFT−. The insulating,filtering, and heat flux control techniques shown in FIG. 6A-FIG. 6C mayoptionally be used for some or all NITI sensor embodiments.

Referring to FIG. 7A, example CHFT+ embodiments include a heat fluxsensor, a temperature sensor, and an external thermal device, e.g., aheater, a cooler, a fluid flow channel, a fan, a heat lamp, etc. that isused with a control circuitry intended for NITI. CHFT+ embodiments areparticularly useful when external thermal events do not occur and, forthe most part, steady-state conditions are maintained. However, they mayalso be used in situations where an uncontrolled external thermal eventis occurring. With the external thermal device, the CHFT+ can generate acontrolled thermal event that creates a transient response (i.e.,differing thermal signals). For example, the external thermal device cancycle heater (i.e., an external thermal device) power to provide aperiodic thermal event at an object surface. When needed, externalthermal devices can be controlled to achieve steady-state conditions. Inother example embodiments, a CHFT+ may include more than one externalthermal device. For example, both a heater and a Peltier cooler may beutilized as external thermal devices in order to create thermal heatsources and thermal heat sinks as desired. As another example, a singlePeltier device may be used as the external thermal device to achieveboth thermal heating and cooling. In FIG. 7A, a heater is illustrated asan example of an external thermal device. In this example, the heater(i.e., the external thermal device) is designed to provide the thermalevent to an area encompassing the entirety of the heat fluxsensor-temperature sensor pair as well as object surface areassurrounding the heat flux sensor-temperature sensor pair. In FIG. 7B,another example embodiment is illustrated where the heater (e.g., theexternal thermal device) is designed to provide the thermal event to anarea encompassing the entirety of the heat flux sensor-temperaturesensor pair only. A top view of an example CHFT+ embodiment is shown inFIG. 7C which includes a temperature sensor with output leads (i.e.,output terminal connection), a heat flux sensor with output leads(example output terminals), and a heater (an example external thermaldevice) with power leads (example power terminals). In this example, theoutput and power leads are connected (e.g., soldered) to thecorresponding output terminals of each component. In other exampleembodiments, the output terminals may be connected to other terminals(e.g., electrically conductive pads) designed for surface mounted orthrough-hole devices, e.g., by using rigid and/or flex printed circuitboard technologies. In other example CHFT+ embodiments, a heater may beconstructed within, for example, a printed circuit board via tracepatterns with controlled resistance, shape, and/or size that directlyconnect to a power source within the circuitry. This may easemanufacturing processes given the embedded aspect of such a design. Insome example NITI sensor embodiments, one or more of the temperaturesensor output leads may be connected to a ground terminal and/orreference resistor that may be used as a part of circuitry to maketemperature measurements based on a temperature sensor resistance (e.g.,thermistor).

In other example embodiments, such as illustrated in FIG. 7D, thetemperature sensor may be located on or near the opposite side of theheat flux sensor sensing area that is in contact with the objectsurface. In these example embodiments, the output of the temperaturesensor may be assumed to be the same as the output of a temperaturesensor as configured in FIG. 7A. This is especially the case when theheat flux sensor has a negligible thermal resistance as a result of itsdesign (e.g., low thickness, high thermal conductivity, etc.) and/orwhere a zero heat-flux condition is created. In other exampleembodiments, for example embodiments where the thermal resistance of theheat flux sensor may not be negligible, the one or more effects of theheat flux sensor's thermal resistance may be modeled as a part of thethermal contact resistance between the temperature sensor and objectsurfaces. In other example embodiments, for example, embodiments wherethe number of heat flux sensor junctions and heat flux sensorsensitivity are accurately known, the heat flux sensor output may beused to determine the temperature difference across the heat flux sensorin real-time such that the output may be combined with the temperaturesensor in FIG. 7D to determine the temperature between the heat fluxsensor and object surface.

In other example embodiments, such as illustrated in FIG. 7E, thetemperature sensor may be embedded within the heat flux sensor and/orthe heat flux sensor sensing area.

In other example embodiments, such as illustrated in FIG. 7F, the heatflux sensor and temperature sensor may be located on either side of asubstrate while avoiding a mismatch of measurements. For example, theheat flux sensor and temperature sensor may be aligned on either side ofa substrate (e.g., a flexible printed circuit board) such that the heatflux sensor and/or the heat flux sensor sensing area encompass thetemperature sensor on the opposing side. This may be achieved by, forexample, placing the heat flux sensor beneath or on top of thetemperature sensor that is on the opposing side of the substrate. Inthese example embodiments, the heat flux sensor and/or temperaturesensor may be further surrounded by and/or in contact with otherthermally compatible materials (e.g., materials with thermal resistancesclose to the temperature/or heat flux sensor) to ensure a uniformthermal energy flow (e.g., heat flow) through the heat flux sensor andtemperature sensor. An example embodiment is illustrated in FIG. 7G.

The non-limiting features of the example embodiments illustrated in FIG.7D-FIG. 7G may optionally be used in any example NITI embodiments,including example CHFT− embodiments.

System Embodiments with One or More Heat Flux Sensor-Temperature SensorPairs for Determining One or More Internal Properties of an Object

FIG. 8 illustrates an example NITI system to perform NITI using theCHFT−. The CHFT− includes a temperature sensor and a heat flux sensor(i.e., a heat flux sensor-temperature sensor pair). In other exampleembodiments, the CHFT− may include more than one temperature sensorand/or more than one heat flux sensor (e.g., multiple heat fluxsensor-temperature sensor pairs). The configuration of the temperaturesensor and the heat flux sensor with respect to each other and theobject may be, for example, as illustrated in any of FIGS. 5 and 6A-6C.Analog signal outputs from the temperature sensor and the heat fluxsensor corresponding to measured temperature sensor and measured heatflux sensor analog signals are provided via suitable communication paths(e.g., electrical conductors) and converted to digital signals by dataacquisition (DAQ) circuitry, which may include, for example, one or moreanalog-to-digital converters (ADCs), microcontrollers, etc. The DAQcircuitry provides measured temperature sensor and measured heat fluxsensor digital signals via suitable communication paths (e.g.,electrical conductors, radio signals, etc.) to control circuitry forprocessing as described in more detail below. The control circuitry mayinclude one or more suitably configured computers, microprocessors,DSPs, FPGAs, or other data processors. Suitable configuration of thecontrol circuitry may be implemented in hardware, in software, or acombination. The control circuitry includes or is in communication withan output such as a display, a network, a cloud computer system, acommunications device like a cell phone, wearable technology, etc. Theoutput may also be used for one or more control operations such assensor enablement and disablement, remote monitoring, measurementstart/stop, data logging, temperature control, energy control, systemfailure control, preventive maintenance control, diagnostics, systemperformance, data input, data display, analytics, etc.

FIG. 9 illustrates an example NITI system to perform NITI with a CHFT+.Like the CHFT−, the CHFT+ includes a temperature sensor and a heat fluxsensor (i.e., a heat flux sensor-temperature sensor pair). In otherexample embodiments, the CHFT+ may include more than one temperaturesensor and/or more than one heat flux sensor (e.g., multiple heat fluxsensor-temperature sensor pairs). In addition, the CHFT+ includes anexternal thermal device such as a resistive heater shown. Theconfiguration of the temperature sensor, the heat flux sensor, and theexternal thermal device with respect to each other and the object maybe, for example, as illustrated in any of FIGS. 7A-7G. In other exampleembodiments, the CHFT+ may include more than one external thermal device(e.g., a heater and a cooler). Analog signal outputs from thetemperature sensor and the heat flux sensor corresponding to measuredtemperature sensor and measured heat flux sensor analog signals areprovided via suitable communication paths (e.g., electrical conductors)and converted to digital signals by data acquisition (DAQ) circuitry,which may include, for example, one or more analog-to-digital converters(ADCs), microcontrollers, etc. The DAQ circuitry provides measuredtemperature sensor and measured heat flux sensor digital signals viasuitable communication paths (e.g., electrical conductors, radiosignals, etc.) to control circuitry for processing as described in moredetail below. The control circuitry may include one or more suitablyconfigured computers, microprocessors, DSPs, FPGAs, or other dataprocessors. Suitable configuration of the control circuitry may beimplemented in hardware, in software, or a combination. The controlcircuitry includes or is in communication with an output such as adisplay, a network, a cloud computer system, a communications devicelike a cell phone, wearable technology, etc. The output may also be usedfor one or more control operations such as sensor enablement anddisablement, remote monitoring, measurement start/stop, external thermaldevice operation, data logging, temperature control, energy control,system failure control, preventive maintenance control, diagnostics,system performance, data input, data display, analytics, etc. In thisnon-limiting example, the external thermal device is controlled using arelay (an example switch), and the relay is operated by a relay signalfrom the DAQ which in turn provides the relay signal based on input fromthe control circuitry.

FIG. 10 is a flowchart outlining example procedures performed by thecontrol circuitry in a non-limiting and example NITI system thatincludes a NITI sensor for determining one or more internal propertiesof an object, including an internal temperature distribution of theinternal region of the object at one or more specified times usingmeasured heat flux, measured temperature, and determined values ofinternal parameters of the object. A measured temperature signal isreceived by the control circuitry from the temperature sensor at one ormore specified times (step S1). The control circuitry also receives ameasured heat flux signal from the heat flux sensor measured at the oneor more specified times to produce a measure of the heat transferleaving or entering the object at the surface (step S2). The controlcircuitry determines values of the internal parameters at the one ormore specified times in step S3 and determines an internal temperaturedistribution of the internal region of the object at the one or morespecified times based on the measured temperature signal, the measuredheat flux signal, and the values of the internal parameters in step S4.The control circuitry generates information (e.g., for output)indicating the internal temperature distribution at the one or morespecified times (step S5). The control circuitry also generatesinformation (e.g., for output) indicating one or more of the internalparameters at the one or more specified times in step S6. The controlcircuitry may optionally perform step S6 before step S5 and/or mayoptionally not perform step S4, step S5, and/or step S6. The controlcircuitry may optionally perform step S2 before step S1. In some exampleembodiments, the control circuitry may optionally perform step S3 beforestep S2 and/or step S1.

Additional procedures may be used in further example embodiments. Forexample, a thermal mathematical model (i.e., thermal model) of theobject is determined and appropriate initial and boundary conditions areprescribed in order to solve for a thermal mathematical solution (i.e.,mathematical solution). Thermal mathematical models and correspondingthermal mathematical solutions may be found in heat transfer literaturefor more general cases, while models for more unique cases may need tobe derived and solved. A variety of methods for deriving and/or solvinga thermal mathematical model may be used, including, but not limited to,analytical methods, finite difference methods, numerical methods, etc.Thermal mathematical models may be based on one-dimensional heattransfer or multi-dimensional heat transfer (e.g., two-dimensional).

For more accurate, robust, and consistent NITI, the boundary conditionsof the thermal mathematical model are defined to include a surface heatflux boundary condition resulting in a thermal mathematical solution(e.g., internal temperature distribution) for the object with a heatflux input. A surface heat flux boundary condition can be used becausethe NITI sensor directly measures heat flux using, for example, a heatflux sensor at the object surface. Thus, heat flux can be directly usedin the thermal mathematical model (i.e., heat flux boundary condition)which results in a heat flux input in the corresponding thermalmathematical solution (i.e., mathematical solution). Table 1 provides adetailed but still example one-dimensional thermal mathematical model(i.e., thermal model) which includes, a partial differential equation(PDE), appropriate boundary conditions, and an initial condition for asemi-infinite solid (i.e., semi-infinite medium), an example object anda general case in heat transfer literature.

TABLE 1 Thermal Model of a Semi-Infinite Solid with Heat Flux BoundaryCondition PDE$\frac{\partial T}{\partial t} = {\alpha\frac{\partial^{2}T}{\partial x^{2}}}$Boundary Conditions${{{- k}\frac{\partial T}{\partial x}} = {q_{Sensor}^{''}(t)}},$ x = 0 T→ T₀, x →∞ Initial Condition T = T₀, t = 0 where: k = thermalconductivity of the object ρ = density of the object C = specific heatcapacity of the object α = thermal diffusivity of the object x = depthfrom object surface t = time T = internal temperature distribution ofthe object (a function of x and t) T₀ = initial temperature of theobject

For a constant step heat flux input that occurs at the surface (x=0) ofthe semi-infinite medium (object), the mathematical solution of thethermal model in Table 1 is found as:

$\begin{matrix}{{T\left( {x,t} \right)} = {T_{0} + {\frac{2{q_{{Se{nsor}},0}^{''}\left( \frac{\alpha t}{\pi} \right)}^{\frac{1}{2}}}{k}{\exp\left( \frac{- x^{2}}{4\alpha t} \right)}} - {\frac{q_{{S{ensor}},0}^{''}x}{k}{{erfc}\left( \frac{x}{2\sqrt{\alpha t}} \right)}}}} & \lbrack 2\rbrack\end{matrix}$

where q_(Sensor,0)″ is the constant step heat flux input at theboundary.

Using the Duhamel Method of Superposition (an example mathematicalmethod), Equation [2] can be derived for heat flux inputs that changewith time which is realistic of NITI sensor output:

$\begin{matrix}{{T_{m}\left( {x,t_{m}} \right)} = {T_{0} + {\sum\limits_{j = 1}^{m}{\left( {q_{{Sen{sor}},j}^{''} - q_{{Se{nsor}},{j - 1}}^{''}} \right)\left( {{\frac{2\left( \frac{\alpha\left( {t_{m} - t_{j - 1}} \right)}{\pi} \right)^{\frac{1}{2}}}{k}{\exp\left( \frac{- x^{2}}{4{\alpha\left( {t_{m} - t_{j - 1}} \right)}} \right)}} - {\frac{x}{k}{{erfc}\left( \frac{x}{2\sqrt{\alpha\left( {t_{m} - t_{j - 1}} \right)}} \right)}}} \right)}}}} & \lbrack 3\rbrack\end{matrix}$

where m indicates the m^(th) measurement made by the NITI sensor so thatT_(m)(x,t_(m)) refers to the internal temperature of the object at adepth of x and at the m^(th) measurement which corresponds to aspecified time (t_(m)).

In this example, Equation [3] represents the thermal mathematicalsolution, i.e., the mathematical expression for the internal temperaturedistribution of the internal region of the object, for the non-limitingand example thermal model specified in Table 1.

Evaluating Equation [3] at the surface (x=0) and realizing that

$\begin{matrix}{\alpha = {{\frac{k}{\rho C}:T_{Surface}} = {T_{{Surface},0} + {\sum\limits_{j = 1}^{m}{\left( {q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}} \right) \times \sqrt{t_{m} - t_{j - 1}} \times \frac{2}{\sqrt{\pi}\sqrt{k\rho C}}}}}}} & \lbrack 4\rbrack\end{matrix}$

where T_(Surface,m) is the calculated surface temperature of the exampleobject modeled in Table 1. Note that in this example, Equation [4] is afunction of the surface object temperature in steady-state conditions(T_(Surface,0)) and is determined, e.g., prior to or after a transientthermal event. Equation [4] is also a function of surface heat fluxmeasurements at one or more specified times (q_(Sensor,m)″) and thesquare root of the product of object thermal conductivity (k), objectdensity (ρ), and object specific heat capacity (C). This internalparameter of the object (√{square root over (kρC)}) is commonly referredto as thermal inertia (i.e., thermal effusivity).

The calculated object surface temperature as determined in Equation [4]can be used with a data processing method that may include, for example,one or more parameter estimation schemes. For NITI sensor output values(i.e., heat flux and temperature) measured at one or more specifiedtimes, the data processing method may compare the measured sensortemperature against the calculated surface temperature as found, in thisexample, when using Equation [4]. Among other things, this allows forthe determination of estimated values for the corresponding internalparameters of the object; in this case, the internal parameter ofthermal inertia (i.e., thermal effusivity) of the object (√{square rootover (kρC)}).

In other data processing methods, estimated values for the internalparameters of, in this example, object thermal conductivity (k), objectdensity (ρ), and object specific heat capacity (C) may be determinedindividually. For example, for the case presented above, predeterminedvalues of density (ρ) and specific heat capacity (C) may be determinedfrom reference materials such as a textbook or manufacturespecification, allowing for a data processing method to determine anestimated value for thermal conductivity (k) based on the estimatedvalue of thermal inertia (i.e., thermal effusivity) of the object((√{square root over (kρC)})) or kρC. In other examples, a differentthermal mathematical model may be developed with a corresponding thermalmathematical solution that, as opposed to Equation [4], distinguishesbetween each individual internal parameter when evaluated at a depth (x)in the object (e.g., x=0). This would allow for the determination ofestimated values for each individual internal parameter (e.g., k, ρ, C,etc.) when used with an appropriate data processing method. The controlcircuitry may also perform further steps to improve the accuracy and/orexpand the applications of NITI sensor(s). For example, as mentionedprior, the measured sensor temperature is not the same as a measure ofthe actual surface temperature of the object (e.g., semi-infinite solid)due to the presence of thermal contact resistance (R_(C)″) between thetemperature sensor and object surface. This causes a difference betweenthe actual surface temperature of the object and the measured sensortemperature. Thermal contact resistance (R_(C)″) may result frommaterials that may be layered over the temperature sensor of a NITIsensor as well as how well it adheres to the object surface. Thesmoothness/roughness of the object surface can also affect the thermalcontact resistance (R_(C)″) as well as the overall accuracy of NITI.Thus, a smooth surface may be preferred. Use of adhesives (e.g., thermalpaste, pressure sensitive adhesives, etc.) to mount the sensor may alsoaffect thermal contact resistance (R_(C)″). FIG. 4 illustrates thermalcontact resistance (R_(C)″) as pertains to an example NITI embodiment.

Mathematically, the measured sensor temperature and actual surfacetemperature can be related by Equation [1], shown here in index form as:

T _(Surface,m) =T _(Sensor,m) −q _(Sensor,m) ″×R _(C)″  [5]

where heat flux is defined to be positive when entering the object.In an electrical engineering analogy, thermal contact resistance(R_(C)″) may be modeled as a resistor and q_(Sensor,m)″ as current.Thus, as current (q_(Sensor,m)″) flows through the resistor (R_(C)″), avoltage drop (difference) is created. Here, the voltage difference isanalogous to a temperature difference between the sensor (i.e.,measured) and object (i.e., actual) surface temperatures.

In some cases, the thermal effects associated with materials used tomount the sensor may also need to be considered. For example, one ormore effects associated with, for example, mounting material thermalconductivity (k), mounting material density (ρ), and mounting materialspecific heat capacity (C) may need to be included and accounted for ina thermal mathematical model used for NITI.

For more accurate NITI, the effects of thermal contact resistance(R_(C)″) should be taken into account. Using Equation [4] with Equation[5] produces an expression for calculated sensor temperature in Equation[6].

$\begin{matrix}{T_{{Calculated},m} = {T_{{Sen{sor}},0} - {q_{{sensor},0}^{''} \times R_{C}^{''}} + {\sum\limits_{j = 1}^{m}{\left( {q_{{Sensor},j}^{''} - q_{{Sen{sor}},{j - 1}}^{''}} \right) \times \sqrt{t_{m} - t_{j - 1}} \times \frac{2}{\sqrt{\pi}\sqrt{k\rho c}}}} + {q_{{sen{sor}},m}^{''} \times R_{C}^{''}}}} & \lbrack 6\rbrack\end{matrix}$

Instead of Equation [4], Equation [6] may be used in a data processingmethod and, for example, compared against the measured sensortemperature output from the NITI sensor in order to determine estimatedvalues for one or more internal parameters of the object. One exampleand non-limiting method of doing this is to define an objective functionfor minimization in a parameter estimation scheme. An example objectivefunction could be defined as the Root Mean Squared Error (RMSE) betweenthe two different measures of sensor temperature using Equation [7].

$\begin{matrix}{{RMSE} = \sqrt{\frac{1}{M - 1}{\sum\limits_{m = 1}^{M - 1}\left( {T_{{Sensor},m} - T_{{Calculated},m}} \right)^{2}}}} & \lbrack 7\rbrack\end{matrix}$ where $\begin{matrix}{T_{{Calculated},m} = {T_{{Surface},m} + {q_{{Sensor},m}^{''} \times R_{C}^{''}}}} & \lbrack 8\rbrack\end{matrix}$

Thus, Equation [7] can be rewritten as:

$\begin{matrix}{{RMSE} = \sqrt{\frac{1}{M - 1}{\sum\limits_{m = 1}^{M - 1}\left( {T_{{Sensor},m} - \left( {T_{{Surface},m} + {q_{{Sensor},m}^{''} \times R_{C}^{''}}} \right)} \right)^{2}}}} & \lbrack 9\rbrack\end{matrix}$

where M is the total number of measurements made by the NITI sensor overa period of time (i.e., one or more specified times). It should be notedthat, depending on the embodiment, m may not always begin at the valueof 1 as shown in Equation [7] and Equation [9]. Similarly, the quantityM−1 may also differ depending on the embodiment. For example, M−1 couldbe replaced by M−15 or M. In other example embodiments, M−1 may bereplaced by m+30, m+10, m+5, etc. which defines the objective functionfor a specified number of measurements after the Mt h measurement.

In other data processing methods, a formulation based on the derivativeof the objective function (e.g., Equation [9]) may be, for example, setequal to zero. The values of corresponding internal parameters andthermal contact resistance (R_(C)″) that best satisfy this condition arethe determined estimated values.

As iterated prior, a major component of accurate and practical NITI isthermal contact resistance (R_(C)″) determination. For some cases, forexample, low heat flux environments (e.g., zero heat-flux conditions) orotherwise negligible thermal contact resistance (R_(C)″) conditions, thethermal contact resistance (R_(C)″) may be ignored or otherwisedetermined to have an estimated value of zero. But for many cases, thisis not an accurate assumption. In these cases, an estimated value forthermal contact resistance (R_(C)″) may, for example, need to bedetermined beforehand through previous measurement, determined as a partof a data processing method (e.g., via a parameter estimation scheme),or otherwise determined (e.g., predetermined by manufacturespecification).

One way to determine an estimated value of thermal contact resistance(R_(C)″) is to include it as an unknown variable in a data processingmethod that may include a parameter estimation scheme. The combinationof corresponding internal parameter values and thermal contactresistance (R_(C)″) value that generate the best match between thecalculated sensor temperature and the measured sensor temperature, i.e.,a least error, may be deemed to be the determined estimated values(i.e., optimal output values).

For example, for the general and example semi-infinite object casepresented above, for each value attempted (e.g., guessed) for √{squareroot over (kρC)}, an array of different R_(C)″ values is also attemptedand input into Equation [6]. For each combination of attempted √{squareroot over (kρC)} and R_(C)″ values, the result of Equation [6] (i.e.,calculated sensor temperature) is compared against the measured sensortemperature as output by the NITI sensor. This comparison can beconducted via, for example, an objective function such as the onedefined in Equation [7]. In this example, the combination of valuesattempted for the internal parameters (e.g., √{square root over (kρC)})and thermal contact resistance (R_(C)″) that generate the best matchbetween the calculated sensor temperature and the measured sensortemperature, i.e., a least error (e.g., least RMSE value), may be deemedto be the determined estimated values (i.e., optimal output values).However, this example approach (i.e., a brute force data processingmethod) may be time consuming, especially when more accurate results aredesired. Consequently, this approach makes a majority of NITIapplications impractical. Although time consuming, this technique ismore accurate and faster than a brute force data processing method thatis based on a mathematical solution found using a temperature basedboundary condition. This is a result of the complexities and limitationsof temperature based boundary conditions.

Another approach is to determine estimated values of the correspondinginternal parameters (e.g., √{square root over (kρC)}) and the thermalcontact resistance (R_(C)″) value via an optimization scheme. Forexample, an optimization scheme may be designed to minimize theobjective function (e.g., Equation [7]) by, for example, non-linearlyvarying combinations of the internal parameter values (e.g., √{squareroot over (kρC)}) and the thermal contact resistance (R_(C)″) value.This approach could yield faster results when compared to the bruteforce data processing method described above but may not be as accurate.

A novel approach to determine an estimated value for thermal contactresistance (R_(C)″) is to determine (e.g., calculate) it based on theinternal properties of the object. This significantly reduces processingtime and makes the technology more practical for many applications. Thisapproach takes advantage of the thermal contact resistance (R_(C)″)being constant with respect to time. Thus, at any specified time or atany given measurement, the thermal contact resistance (R_(C)″) isequivalent to the thermal contact resistance (R_(C)″) at preceding orfollowing specified times or measurements. Mathematically this can beexpressed as:

R _(C) ″=R _(C) _(n) ″  [10]

where n indicates the n^(th) measurement made by the NITI sensor (totalof N measurements during a period of time). Thus, for purposes of thisnon-limiting example, N=M. Furthermore, the quantity n may differdepending on the embodiment. For example, n could be replaced by n−1 orn+1.

Given this consistency, the thermal contact resistance (R_(C)″) at aspecified time or measurement is equivalent to the average thermalcontact resistance throughout the period of time for which measurementsare being made and can be expressed as:

$\begin{matrix}{R_{C_{n}}^{''} = \frac{{\Sigma}_{n = 1}^{N - 1}R_{C_{n}}^{''}}{N - 1}} & \lbrack 11\rbrack\end{matrix}$

Furthermore, Equation [5] can be rearranged as:

$\begin{matrix}{R_{C_{n}}^{''} = \frac{T_{{Sensor},n} - T_{{Surface},n}}{q_{{Sensor},n}^{''}}} & \lbrack 12\rbrack\end{matrix}$

Combining Equation [10], Equation [11], and Equation [12] produces:

$\begin{matrix}{R_{C_{n}}^{''} = \frac{{\Sigma}_{n = 1}^{N - 1}\frac{T_{{S{ensor}},n} - T_{{Surface},n}}{q_{{Sensor},n}^{''}}}{N - 1}} & \lbrack 13\rbrack\end{matrix}$

With regard to the example data processing method described prior,inputting Equation [13] into Equation [9], an example objective functionof a parameter estimation scheme, results in:

$\begin{matrix}{{RMSE} = \sqrt{\begin{matrix}{\frac{1}{M - 1}{\sum\limits_{m = 1}^{M - 1}\left( {T_{{Sen{sor}},m} - \left( {T_{{Surf{ace}},m} +} \right.} \right.}} \\\left. \left. {q_{{Sensor},m}^{''} \times \frac{{\sum}_{n = 1}^{N - 1}\frac{T_{{Sen{sor}},n} - T_{{Surf{ace}},n}}{q_{{Sensor},n}^{''}}}{N - 1}} \right) \right)^{2}\end{matrix}}} & \lbrack 14\rbrack\end{matrix}$

It should be noted that, depending on the example embodiment, n may notalways begin at the value of 1 as shown in Equation [14]. Similarly, thequantity N−1 may also differ depending on the embodiment. For example,N−1 could be replaced by N−15 or N. In other example embodiments, N−1may be replaced by n+30, n+10, n+5, etc. which defines Equation [13] fora specified number of measurements after the n^(th) measurement.

Compared to Equation [9], this version of the example objective functionin Equation [14] is largely independent of the thermal contactresistance (R_(C)″). The only term that is dependent on the thermalcontact resistance (R_(C)″) is T_(Surface,0) where, as a result ofEquation [5], is defined as T_(Sensor,0)−q_(Sensor,0)″×R_(C)″. It shouldbe noted that, in many cases, the quantity q_(Sensor,0)″×R_(C)″ may benegligible. In cases where it is not negligible, a better design isneeded and the quantity q_(Sensor,0)″×R_(C)″ may need to be accountedfor. An example method of achieving this is by attempting (e.g.,guessing) an initial value for thermal contact resistance (R_(C)″)before conducting, in this data processing method example, a parameterestimation scheme. Regardless of the initial value attempted, theparameter estimation scheme will determine an accurate estimated valuefor thermal contact resistance (R_(C)″) as well as accurate estimatedvalues for the internal parameters.

As a part of a data processing method, using Equation [14] as theobjective function in a parameter estimation scheme greatly reduces thetime needed to make NITI measurements. For comparable accuracy and usingthe same computer, the inventor determined that this data processingmethod may be completed in less than 1 second of processing time ascompared to approximately 15 minutes when utilizing a data processingmethod based on the brute force approach described above for the samedata set (75 seconds of data-1 HZ sampling frequency).

Finally, another non-obvious approach is to determine an estimated valuefor the thermal contact resistance (R_(C)″) based on the internalparameters and the overall steady-state thermal resistance (R_(Total)″)of a given object. A non-limiting example of this is described below foran example NITI application.

It should be noted that these approaches for thermal contact resistance(R_(C)″) determination are not limited to a specific data processingmethod and/or NITI technique. Instead, they can be used as generalexpressions and approaches for thermal contact resistance (R_(C)″)determination regardless of the data processing method being utilizedfor NITI and/or NITI application.

FIG. 11 is a flow diagram showing non-limiting example procedures for anexample data processing method performed by the control circuitry inorder to determine one or more internal properties of an object (i.e.,internal properties) and an estimated thermal contact resistance(R_(C)″) between the object and NITI sensor surfaces. In this example,the data processing method includes a parameter estimation scheme.Measured surface temperature (i.e., measured sensor temperature) for theobject at one or more specified times, measured surface heat flux forthe object at the one or more specified times, initial values for one ormore of the internal parameters of the object (e.g., R″ (thesteady-state thermal resistance of the object), k, ρ, C, √{square rootover (kρC)}, etc.) at the one or more specified times, and an initialvalue for the thermal contact resistance (R_(C)″) are input to acalculated sensor temperature equation (e.g., Equation [6]) to generatea calculated sensor temperature for the one or more specified times. Inthis example, a difference (e.g., error) is determined between thecalculated sensor temperature for the one or more specified times andthe measured sensor temperature for the one or more specified times. Thedifference is, for example, compared to a predetermined threshold and ifgreater than the threshold, then the difference is used to adjust one ormore of the internal parameter values and thermal contact resistance(R_(C)″) value. For simplicity, the one or more adjusted internalparameter values and the one or more other (i.e., non-adjusted) internalparameter values are collectively referred to as updated values.Adjustment can be made in a number of different ways. For example,subsequent values of one or more of the internal parameters and thethermal contact resistance (R_(C)″) can be used without regard for anytrends or patterns in the historical difference (e.g., error) resultingfrom the internal parameter and thermal contact resistance (R_(C)″)values used prior. In other examples, adjustments can be made based onthe historical difference (e.g., error) resulting from the internalparameter and thermal contact resistance (R_(C)″) values used prior. Ina non-limiting example, if a value of k (e.g., k₀) relates to adifference (i.e., error) of 100, and the next value, a greater value,used for k (e.g., k₁) relates to an error of 200, the control circuitrymay attempt a value less than the original value of k (k₀) given thedifference (i.e., error) increased when using a value greater than k₀(k₁). Once the difference is less than or equal to the threshold orotherwise deemed minimal, the control circuitry deems the correspondingvalues used for the internal parameters and the thermal contactresistance (R_(C)″) to be accurate and optimal (i.e., output) estimatedvalues. Then by using, for example, Equation [3], the control circuitrygenerates information (e.g., for output) corresponding to one or moreaccurate value(s) indicating the internal temperature distribution ofthe internal region of the object. Furthermore, if desired, the controlcircuitry generates information (e.g., for output) corresponding toaccurate estimated value(s) indicating one or more of the internalparameters for the object such as R″, k, ρ, C, √{square root over(kρC)}, etc. and the thermal contact resistance (R_(C)″).

The approach just described is a non-limiting example periodic NITI dataprocessing method performed by the control circuitry that may determinethe internal parameters (e.g., R″, k, ρ, C, √{square root over (kρC)},etc.) of the object, the thermal contact resistance (R_(C)″) between thetemperature sensor and object surfaces, the internal temperaturedistribution of the internal region of the object (e.g.,T_(m)(x,t_(m))), etc. by post processing the heat flux and temperaturesignals output from a NITI sensor placed on the surface of the objectand while may be subject to a thermal event. For the CHFT+, this thermalevent can be generated by, for example, an external thermal device usedwith the control circuitry. While the CHFT− is designed to operate, forexample, under external thermal event environments such as heatdissipation from the body, engine block heat loss, convective cooling orheating, etc. that are not used with the control circuitry. Because thisprocedure can be performed so quickly by the control circuitry, the dataprocessing can be performed in real time as the heat flux andtemperature signals are being measured and provided as inputs to thecontrol circuitry. With each additional measurement, the data processingmethod is rerun, values for one or more of the internal properties ofthe internal region of the object (i.e., internal properties) aredetermined, and information for output, for example, is generated.

Other methods (i.e., techniques) of NITI may be performed by, forexample, modifying the thermal mathematical solution (e.g., Equation[3]) to different forms depending on the internal properties ofinterest. Non-limiting examples of modified arrangements of thermalmathematical solutions and corresponding NITI methods are provided belowfor different applications. Each of these applications havecorresponding thermal mathematical models. In general, depending on theNITI application and procedure used, different data processing methodsmay be utilized to determine estimated values for one or more internalproperties of an object. Some of these methods may utilize parameterestimation schemes while others may not and instead, for example, bebased on a calculation.

In other example embodiments, various mathematical operations may beperformed on, for example, the thermal mathematical solution (e.g.,derivate operations, integral operations, etc.) to determine (e.g., viaa data processing method), one or more internal properties of an object.

System Embodiments with One or More Parallel Heat FluxSensor-Temperature Sensor Pairs for Determining One or More InternalProperties of an Object

Example NITI system embodiments that acquire object heat flux andtemperature measurements in parallel by multiple (at least two) NITIsensors (e.g., CHFT+ or CHFT−) are referred to as DUO NITI embodiments.In addition to allowing for simpler and more robust NITI of objects, theDUO NITI embodiments eliminate uncertainties that may be associated withthe non-limiting example NITI system embodiments and/or methodsdescribed above for the example CHFT+ and/or example CHFT− NITI systemembodiments.

In order to make measurements in parallel, each NITI sensor in exampleDUO NITI embodiments may have different heat flux values detected byeach heat flux sensor, corresponding to a difference in the amount ofheat flux occurring at each NITI sensor location, also called a sensornode. This aspect of example DUO NITI embodiments is referred to as adifferential heat flux environment. Example embodiments below may beused to achieve this condition. Typically, as a result of thedifferential heat flux environment, temperature measurements at eachsensor node (i.e., node) also differ.

One way to create a differential heat flux environment with an exampleDUO CHFT+ embodiment (multiple CHFT+ nodes) is to vary the amount ofthermal energy each CHFT+ external thermal device (e.g., heater)provides. In the case of a heater, this can be achieved by, for example,differentiating the voltage provided to each heater, differentiating theelectrical resistance of each heater, differentiating the power densityof each heater, etc. to create the differential heat flux environmentneeded. FIG. 12 shows a cross-section of an example DUO (parallel NITIsensor nodes) CHFT+(with a heater) embodiment. In this exampleembodiment, each NITI sensor (i.e., sensor node or node) contains oneheat flux sensor-temperature sensor pair and includes a heater (i.e.,external thermal device) as a result of being CHFT+ nodes.

If an external thermal device (e.g., heater) is not an option, desired,or used, another way to create a differential heat flux environment isto place differing amounts of thermal insulation on each sensor node.The insulation can be used to control (i.e., limit, increase, etc.) theamount of heat flux occurring through the sensor node. Differing amountsof thermal insulation could be achieved via differing insulationthickness and/or materials. Thermal insulation may include metals orother thermally conductive materials designed to enhance and increasethe amount of heat transfer occurring through the sensor node.Furthermore, the insulation may act as a filter and only allowsubstantive heat flux and temperature signals to be detected by the NITIsensor (e.g., CHFT+ or CHFT−). The insulation may also be used toprotect the NITI sensor from external damage and/or external stimulithat may affect the quality of measurement. FIG. 13 shows across-section of an example DUO (parallel NITI sensor nodes) CHFT−embodiment with different amounts of thermal insulation on each sensornode to facilitate a differential heat flux environment. In NITI exampleembodiments, properties of the thermal insulation used at a sensor nodedo not need to be known, experimentally determined, or calibrated tomake measurements of one or more object internal properties.

Alternatively, for example when signal noise may not be an issue, oneCHFT− node may incorporate thermal insulation while the other CHFT− nodeis exposed. The cross-section of this example embodiment is shown inFIG. 14 .

Another example embodiment in FIG. 15 shows the cross-section of a DUOCHFT+/− system where one sensor node incorporates a CHFT+ and one sensornode incorporates a CHFT−.

Still another example embodiment of a DUO CHFT− system cross-section isillustrated in FIG. 16 . This example embodiment may be appropriate incases where external thermal events are specific to individual sensornodes. For example, one sensor node is heated with a lamp while anotheris cooled by a fan.

Another example embodiment in which a differential heat flux environmentis created, includes using materials with different thermal resistancefor each heat flux sensor-temperature sensor pair. For example, onesensor node incorporates an example NITI embodiment (e.g., CHFT−) madewith materials of high thermal resistance and one sensor nodeincorporates an example NITI embodiment (e.g., CHFT−) made withmaterials of low thermal resistance. This difference in overall thermalresistance at each sensor node allows for a differential heat fluxenvironment to be realized. Differing thermal resistance may beintroduced into the example NITI embodiments, for example, by conductiveor insulating vias/gaps within the one or more materials used to adhere,connect, house, and/or contact with the heat flux sensor and/ortemperature sensor (e.g. rigid and/or flex printed circuit board,adhesives, substrates, etc.). In other example embodiments the heat fluxsensor and/or temperature sensor of one sensor node may be manufacturedusing materials of low thermal conductivity and/or specified thicknesswhile the heat flux sensor and/or temperature sensor of another sensornode may be manufactured using materials of high thermal conductivityand/or a different specified thickness.

As a result of the one or more parallel sensor nodes incorporated inexample DUO NITI embodiments, innovative methods of signal measurementand data processing are possible in addition to performing the exampleCHFT+ and example CHFT− methods described above (where sensor nodes areindependently operated). For purpose of demonstration, general,non-limiting, and example differential and quotient based dataprocessing methods are now described for the DUO NITI system whenoperating in differential heat flux environments.

In this example, two NITI sensor nodes (i.e., sensor nodes) are modeledas being placed on a given object, where the internal properties of theobject are, in this example, assumed to be uniform at the two sensornode locations. This results in the following example independentequations at each sensor node (nodes 1 and 2):

$\begin{matrix}{{T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} = {T_{Internal} + {R^{''} \times \left( {q_{{{Sensor}1},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}}} \right)}}} & \lbrack 15\rbrack\end{matrix}$ $\begin{matrix}{{T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} = {T_{Internal} + {R^{''} \times \left( {q_{{{Sensor}2},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}}} \right)}}} & \lbrack 16\rbrack\end{matrix}$

where T_(Internal) is the internal temperature (i.e., internaltemperature distribution) of the object, andψ is a response function that accounts for the transient heat transfereffects of the object at one or more specified times. Typically, p isderived for each thermal model independently and may be based on one ormore internal parameters. Thus, it is typically unique to a given NITIapplication and corresponding thermal model. In some example DUO NITIembodiments, initial values for one or more of the internal parametersat one or more specified times may need to be determined for purposesrelated to the response function (ψ). These initial values may bepredetermined (e.g., from a textbook, reference material, etc.),estimated (e.g., via a data processing method), or otherwise determined.In some example embodiments, the initial values are not changed and keptconstant for the one or more specified times. In other exampleembodiments, the initial values may be updated or otherwise adjusted atone or more specified times.In steady-state form, Equation [15] and Equation [16] reduce to:

T _(Sensor1,m) =T _(Internal,m) +q _(Sensor1,m)″×(R″+R _(C1)″)  [17]

T _(Sensor2,m) =T _(Internal,m) +q _(Sensor2,m)″×(R″+R _(C2)″)  [18]

Note that Equation [17] and Equation [18] do not include the responsefunction (ψ) that accounts for the transient heat transfer effects ofthe object. Thus, they are typically not limited to specific NITIapplications and corresponding thermal models.

A general and example differential based data processing method for theDUO NITI system includes determining the difference between Equation[15] and Equation [16] which results in:

$\begin{matrix}{{\left( {T_{{Se{nsor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - \left( {T_{{Sen{sor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right)} = {{R^{''} \times \left( {q_{{{Sensor}1},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}}} \right)} - {R^{''} \times \left( {q_{{{Sensor}2},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}}} \right)}}} & \lbrack 19\rbrack\end{matrix}$

Rearranging:

$\begin{matrix}{R^{''} = \frac{\begin{matrix}{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) -} \\\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right)\end{matrix}}{\begin{matrix}{q_{{{Sensor}1},0}^{''} - q_{{{Sensor}2},0}^{''} + {{\sum}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times \psi\left( {t_{m} - t_{j - 1}} \right)} -} \\{{\sum}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}\end{matrix}}} & \lbrack 20\rbrack\end{matrix}$

Equation [19] and Equation [20] represent example general forms of theDUO NITI system differential based data processing method wheretransient effects are accounted for and two sensor nodes are used inparallel. In steady-state conditions, Equation [20] reduces to:

T _(Sensor1,m) −T _(Sensor2,m) =q _(Sensor1,m)″×(R″+R _(C1)″)−q_(Sensor2,m)″×(R″+R _(C2)″)  [21]

Rearranging:

$\begin{matrix}{R^{''} = \frac{\begin{matrix}{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) -} \\\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right)\end{matrix}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 22\rbrack\end{matrix}$

In this example data processing method, when the thermal contactresistances at each sensor node (R_(C1)″ and R_(C2)″) are known,Equation [20] and Equation [22] can be used to determine thesteady-state thermal resistance (R″) of the object which is based on,and thus, indicative of, the internal parameters of the object.Consequently, if desired, the steady-state thermal resistance (R″) ofthe object may be used to determine one or more internal parameters ofthe object when values are determined (e.g., predetermined, estimated,etc.) for one or more other internal parameters. Non-limiting examplesof this are provided below.

If an estimated value for the thermal contact resistance at a sensornode (R_(C1)″ and/or R_(C2)″) is unknown, it can be determined (e.g.,via the example CHFT+ or CHFT− procedures described above) or otherwisedetermined (e.g., using predetermined values).

When the thermal contact resistances at each sensor node (R_(C1)″ andR_(C2)″) are estimated to be negligible, Equation [20] reduces to:

$\begin{matrix}{R^{''} = \frac{T_{{{Sensor}1},m} - T_{{{Sensor}2},m}}{\begin{matrix}{q_{{{Sensor}1},0}^{''} - q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}} -} \\{{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}\end{matrix}}} & \lbrack 23\rbrack\end{matrix}$

and Equation [22] reduces to:

$\begin{matrix}{R^{''} = \frac{T_{{{Sensor}1},m} - T_{{{Sensor}2},m}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 24\rbrack\end{matrix}$

When the thermal contact resistances at each sensor node are equal(R_(C)″=R_(C1)″=R_(C2)″), Equation [22] reduces to:

$\begin{matrix}{R_{Total}^{''} = \frac{T_{{{Sensor}1},m} - T_{{{Sensor}2},m}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 25\rbrack\end{matrix}$

where R″_(Total) is the total steady-state thermal resistance of theobject and:

R″ _(Total) =R″+R _(C)″  [26]

A general and example quotient based data processing method for the DUONITI system includes determining the quotient between Equation [15] andEquation [16] which results in:

$\begin{matrix}{\frac{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{Internal}}{\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) - T_{Internal}} = \frac{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)}{\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)}} & \lbrack 27\rbrack\end{matrix}$

Rearranging:

$\begin{matrix}{T_{{internal},m} = \frac{\begin{matrix}{\left( {T_{{Se{nsor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) \times} \\{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right) -} \\{\left( {T_{{Sen{sor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) \times} \\\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)\end{matrix}}{\begin{matrix}{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right) -} \\\left( {q_{{{Sensor}2},j}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)\end{matrix}}} & \lbrack 28\rbrack\end{matrix}$

Equation [27] and Equation [28] represent example general forms of theDUO NITI system quotient based data processing method where transienteffects are accounted for and two sensor nodes are used in parallel. Insteady-state conditions, Equation [27] reduces to:

$\begin{matrix}{\frac{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{Internal}}{\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) - T_{Internal}} = \frac{q_{{{Sensor}1},m}^{''}}{q_{{{Sensor}2},m}^{''}}} & \lbrack 29\rbrack\end{matrix}$

Rearranging:

$\begin{matrix}{T_{{Internal} \cdot m} = \frac{\begin{matrix}{{\left( {T_{{Sen{sor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) \times q_{{{Sensor}1},m}^{''}} -} \\{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) \times q_{{{Sensor}2},m}^{''}}\end{matrix}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 30\rbrack\end{matrix}$

In this example data processing method, when the thermal contactresistances at each sensor node (R_(C1)″ and R_(C2)″) are known,Equation [28] and Equation [30] can be used to determine an internaltemperature distribution (T_(Internal,m)) of the object. If an estimatedvalue for the thermal contact resistance at a sensor node (R_(C1)″and/or R_(C2)″) is unknown, it can be determined (e.g., via the exampleCHFT+ or CHFT− procedures described above) or otherwise determined(e.g., via predetermined values).

When the thermal contact resistances at each sensor node (R_(C1)″ andR_(C2)″) are estimated to be negligible, Equation [28] reduces to:

$\begin{matrix}{T_{{Internal},m} = \frac{\begin{matrix}{{T_{{{Sensor}2},m} \times \left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)} -} \\{T_{{{Sensor}1},m} \times \left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \psi\left( {t_{m} - t_{j - 1}} \right)}} \right)}\end{matrix}}{\begin{matrix}{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times \psi\left( {t_{m} - t_{j - 1}} \right)}} \right) -} \\\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \psi\left( {t_{m} - t_{j - 1}} \right)}} \right)\end{matrix}}} & \lbrack 31\rbrack\end{matrix}$

and Equation [30] reduces to:

$\begin{matrix}{T_{{Internal} \cdot m} = \frac{{T_{{Sensor},m} \times q_{{{Sensor}1},m}^{''}} - {T_{{{Sensor}1},m} \times q_{{{Sensor}2},m}^{''}}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 32\rbrack\end{matrix}$

Equation [32] is also the form of Equation [30] when the thermal contactresistances at each sensor node are equal (R_(C)″=R_(C1)″=R_(C2)″).

As mentioned before, the non-limiting and example transient forms of,for example, the differential and quotient based data processing methodsare typically unique to each NITI application and thermal model giventhe presence of the response function (ψ). However, the steady-stateforms of, for example, the non-limiting and example differential andquotient based data processing methods are typically universal andapplicable for almost any NITI application and corresponding thermalmodel.

FIG. 17 illustrates an example NITI system to perform NITI with parallelheat flux sensor-temperature sensor pairs (i.e., DUO NITI system) fordetermining one or more internal properties of an object. Two NITIsensors (one is referred to as “first” and the other as “second” todistinguish them) are shown (although more than two NITI sensors may beused), and each NITI sensor (e.g., CHFT+ or CHFT−) includes atemperature sensor and a heat flux sensor (i.e., heat fluxsensor-temperature sensor pair). In other example embodiments, each NITIsensor may include more than one temperature sensor and/or more than oneheat flux sensor. The configuration of the temperature sensor and theheat flux sensor for each NITI sensor with respect to each other, toanother NITI sensor, and the object may be as illustrated in any of thenon-limiting examples shown in FIGS. 12-16 . Analog signal outputs fromthe temperature sensor and the heat flux sensor corresponding tomeasured temperature sensor and measured heat flux sensor analog signalsfrom each NITI sensor are provided via suitable communication paths(e.g., electrical conductors) and converted to digital signals by dataacquisition (DAQ) circuitry, which may include, for example, one or moreanalog-to-digital converters (ADCs), microcontrollers, etc. The DAQcircuitry provides measured temperature sensor and measured heat fluxsensor digital signals via suitable communication paths (e.g.,electrical conductors, radio signals, etc.) to control circuitry forprocessing as described above and further below. The control circuitrymay include one or more suitably configured computers, microprocessors,DSPs, FPGAs, or other data processors. Suitable configuration of thecontrol circuitry may be implemented in hardware, in software, or acombination. The control circuitry includes or is in communication withan output such as a display, a network, a cloud computer system, acommunications device like a cell phone, wearable technology, etc. Theoutput may also be used for one or more control operations such assensor enablement and disablement, remote monitoring, measurementstart/stop, external thermal device operation, data logging, temperaturecontrol, energy flow control, system failure control, preventivemaintenance control, diagnostics, system performance, data input, datadisplay, analytics, etc. In this non-limiting example, when applicable(e.g., when using CHFT+ nodes), each external thermal device iscontrolled using a respective relay (i.e., switch), and the relay isoperated by a relay signal from the DAQ which in turn provides the relaysignal based on input from the control circuitry.

FIG. 18A is a flow diagram showing example procedures for a differentialbased data processing method performed by the control circuitry in orderto determine one or more internal parameters of an object (i.e.,internal parameters) using two parallel NITI sensors (one is referred toas “first” and the other as “second” to distinguish them). Measuredsurface temperature at one or more specified times from the temperaturesensor (i.e., measured sensor temperature) in each of the first andsecond NITI sensors and measured surface heat flux at the one or morespecified times from the heat flux sensor in each of the first andsecond NITI sensors are input to the control circuitry. Initial valuesfor one or more of the internal parameters (e.g., R″, k, ρ, C, √{squareroot over (kρC)}, etc.) at the one or more specified times and valuesfor thermal contact resistance at each sensor node (R_(C1)″ and R_(C2)″)are also input to the control circuitry. The control circuitry then usesa differential based data processing method that determines, e.g., basedon Equation [20], one or more of the internal parameters at the one ormore specified times. Finally, the control circuitry generatesinformation (e.g., for output) corresponding to one or more accuratevalue(s) indicating the internal parameters for the object such as R″,k, ρ, C, √{square root over (kρC)}, etc.

FIG. 18B is a flow diagram showing example procedures for a differentialbased data processing method performed by the control circuitry in orderto determine a steady-state thermal resistance of an object (an internalparameter) using two NITI sensors (one is referred to as “first” and theother as “second” to distinguish them) in steady-state conditions.Measured temperature at one or more specified times from the temperaturesensor (i.e., measured sensor temperature) in each of the first andsecond NITI sensors and measured heat flux at the one or more specifiedtimes from the heat flux sensor in each of the first and second NITIsensors are input to the control circuitry. Values for thermal contactresistance at each sensor node (R_(C1)″ and R_(C2)″) are also input tothe control circuitry. The control circuitry then uses a differentialbased data processing method that determines, e.g., based on Equation[22], a steady-state thermal resistance of the object (an internalparameter) at the one or more specified times. Finally, the controlcircuitry generates information (e.g., for output) corresponding toaccurate values indicating the steady-state thermal resistance of theobject. Furthermore, if desired, the control circuitry may generateinformation (e.g., for output) corresponding to one or more accuratevalues indicating one or more of the other internal parameters for theobject such as k, ρ, C, √{square root over (kρC)}, etc., based on thedetermined steady-state thermal resistance of the object and one or moredetermined (e.g., pre-determined, estimated, etc.) internal parameters.

FIG. 19A is a flow diagram showing example procedures for a quotientbased data processing method performed by the control circuitry in orderto determine an internal temperature distribution of the internal regionof an object (i.e., internal temperature distribution) using twoparallel NITI sensors (one is referred to as “first” and the other as“second” to distinguish them). Measured temperature at one or morespecified times from the temperature sensor (i.e., measured sensortemperature) in each of the first and second NITI sensors and measuredheat flux at the one or more specified times from the heat flux sensorin each of the first and second NITI sensors are input to the controlcircuitry. Values for one or more internal parameters (e.g., R″, k, ρ,C, √{square root over (kρC)}, etc.) at the one or more specified timesand values for thermal contact resistance at each sensor node (R_(C1)″and R_(C2)″) and are also input to the control circuitry. The controlcircuitry then uses a quotient based data processing method thatdetermines, e.g., based on Equation [30], the internal temperaturedistribution of the internal region of the object at the one or morespecified times. Finally, the control circuitry generates information(e.g., for output) corresponding to one or more accurate valuesindicating the internal temperature distribution of the internal regionof the object.

FIG. 19B is a flow diagram showing example procedures for a quotientbased data processing method performed by the control circuitry in orderto determine an internal temperature distribution of the internal regionof an object (i.e., internal temperature distribution) using twoparallel NITI sensors (one is referred to as “first” and the other as“second” to distinguish them) in steady-state conditions. Measuredtemperature at one or more specified times from the temperature sensor(i.e., measured sensor temperature) in each of the first and second NITIsensors and measured heat flux at the one or more specified times fromthe heat flux sensor in each of the first and second NITI sensors areinput to the control circuitry. Values for thermal contact resistance ateach sensor node (R_(C1)″ and R_(C2)″) are also input to the controlcircuitry. The control circuitry then uses a quotient based dataprocessing method that determines, e.g., based on Equation [32], theinternal temperature distribution of the internal region of the objectat the one or more specified times. Finally, the control circuitrygenerates information (e.g., for output) corresponding to one or moreaccurate values indicating the internal temperature distribution of theinternal region of the object.

FIG. 20 is a flowchart outlining example procedures performed by thecontrol circuitry in a non-limiting and example NITI system thatincludes a NITI sensor based on parallel NITI sensor nodes (i.e., DUONITI system) and a differential based data processing method fordetermining one or more internal parameters of an object at one or morespecified times. A first measured temperature signal is received by thecontrol circuitry from the temperature sensor in a first non-invasive,heat flux sensor-temperature sensor pair at one or more specified times(step S7). A first measured heat flux signal is received by the controlcircuitry from the heat flux sensor in the first non-invasive, heat fluxsensor-temperature sensor pair at the one or more specified times todetermine a measure of the heat transfer leaving or entering the objectat the surface at the one or more specified times (step S8). A secondmeasured temperature signal is received by the control circuitry fromthe temperature sensor in the second non-invasive, heat fluxsensor-temperature sensor pair at the one or more specified times (stepS9). A second measured heat flux signal is received by the controlcircuitry from the heat flux sensor in the second non-invasive, heatflux sensor-temperature sensor pair measured at the one or morespecified times to determine a measure of the heat transfer leaving orentering the object at the surface at the one or more specified times(step S10). The control circuitry determines initial values for each ofthe internal parameters at the one or more specified times (step S11).The control circuitry then determines one or more of the internalparameters of the object at the one or more specified times based on themeasured temperature signals from the temperature sensors in the firstand second non-invasive, heat flux sensor-temperature sensor pairs atthe one or more specified times, the measured heat flux signals in thefirst and second non-invasive, heat flux sensor-temperature sensor pairsat the one or more specified times, and the initial values of theinternal parameters at the one or more specified times (step S12). Thecontrol circuitry generates information (e.g., for output) indicatingone or more of the internal parameters of the object at the one or morespecified times (step S13). In subsequent procedures performed by thecontrol circuitry (i.e., at one or more future specified times), thecontrol circuitry may determine the initial values for one or more ofthe internal parameters in step S11 based on the values of one or moreof the internal parameters determined in step S12 prior (i.e., at theone or more specified times). Additionally, the control circuitry mayperform step S7 through step S11 in any order and is not limited to theorder specified in this non-limiting example of procedures. Insteady-state conditions, the control circuitry may optionally notperform step S11 and/or may not use initial values of the internalparameters in step S12. Furthermore, the control circuitry may alsoperform steps to determine and account for one or more effectsassociated with a thermal contact resistance between the temperaturesensor in the first non-invasive, heat flux sensor-temperature sensorpair and the surface of the object and/or one or more effects associatedwith a thermal contact resistance between the temperature sensor in thesecond non-invasive, heat flux sensor-temperature sensor pair and thesurface of the object.

FIG. 21 is a flowchart outlining example procedures performed by thecontrol circuitry in a non-limiting and example NITI system thatincludes a NITI sensor based on parallel NITI sensor nodes (i.e., DUONITI system) and a quotient based data processing method for determiningan internal temperature distribution of the internal region of theobject at one or more specified times. A first measured temperaturesignal is received by the control circuitry from the temperature sensorin a first non-invasive, heat flux sensor-temperature sensor pair at oneor more specified times (step S14). A first measured heat flux signal isreceived by the control circuitry from the heat flux sensor in the firstnon-invasive, heat flux sensor-temperature sensor pair at the one ormore specified times to determine a measure of the heat transfer leavingor entering the object at the surface at the one or more specified times(step S15). A second measured temperature signal is received by thecontrol circuitry from the temperature sensor in the secondnon-invasive, heat flux sensor-temperature sensor pair at the one ormore specified times (step S16). A second measured heat flux signal isreceived by the control circuitry from the heat flux sensor in thesecond non-invasive, heat flux sensor-temperature sensor pair measuredat the one or more specified times to determine a measure of the heattransfer leaving or entering the object at the surface at the one ormore specified times (step S17). The control circuitry determines valuesfor each of the internal parameters at the one or more specified times(step S18). The control circuitry then determines the internaltemperature distribution of the internal region of the object at the oneor more specified times based on the measured temperature signals fromthe temperature sensors in the first and second non-invasive, heat fluxsensor-temperature sensor pairs at the one or more specified times, themeasured heat flux signals in the first and second non-invasive, heatflux sensor-temperature sensor pairs at the one or more specified times,and the values of the internal parameters at the one or more specifiedtimes (step S19). The control circuitry generates information (e.g., foroutput) indicating the internal temperature distribution of the internalregion of the object at the one or more specified times (step S20).Additionally, the control circuitry may perform step S14 through stepS18 in any order and is not limited to the order specified in thisnon-limiting example of procedures. In steady-state conditions, thecontrol circuitry may optionally not perform step S18 and/or may not usevalues of the internal parameters in step S19. Furthermore, the controlcircuitry may also perform steps to determine and account for one ormore effects associated with a thermal contact resistance between thetemperature sensor in the first non-invasive, heat fluxsensor-temperature sensor pair and the surface of the object and/or oneor more effects associated with a thermal contact resistance between thetemperature sensor in the second non-invasive, heat fluxsensor-temperature sensor pair and the surface of the object.

Further example procedures performed by the control circuitry in anon-limiting and example NITI system that includes a NITI sensor basedon parallel NITI sensor nodes, may include more than one data processingmethod. For example, a NITI system may include both a differential baseddata processing method and a quotient based data processing method fordetermining (e.g., calculating) one or more internal parameters of anobject and determining (e.g., calculating) an internal temperaturedistribution of the internal region of the object, respectively. TheNITI system may, for example, perform the multiple data processingmethods subsequently or simultaneously. In other example embodiments, adata processing method may be based on a combination of multiple dataprocessing methods to determine one or more internal properties.

Example DUO NITI embodiments may utilize control circuitry to maintainprescribed heat flux and temperature conditions. For example, controlcircuitry can be used to maintain steady-state conditions by adjustingthe power supplied to an external thermal device (e.g., heater). Inother example embodiments, the control circuitry can regulate the amountof heat flux and/or temperature occurring at one sensor node to be aconstant multiple of the heat flux and/or temperature occurring atanother sensor node.

Similar conditions may be further achieved without control circuitry.For example, a prescribed amount of thermal insulation on each sensornode may also be used to regulate the heat flux or temperature occurringat each sensor node to, for example, a constant multiple of anothersensor node.

Creating such environments where the heat flux and/or temperatureoccurring at sensor nodes are related by, for example, a constantmultiple (Y) allows for further simplification of DUO NITI systems anddata processing methods.

For example, if control circuitry and/or thermal insulation is used tomaintain the following relationship between the heat flux occurring ateach sensor node:

Y×q _(Sensor1,m) ″=q _(Sensor2,m)″  [33]

Equation [27] can be rewritten as:

$\begin{matrix}{\frac{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{Internal}}{\left( {T_{{{Sensor}2},m} - {Y \times q_{{{Sensor}1},m}^{''} \times R_{C2}^{''}}} \right) - T_{Internal}} = \frac{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{i = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)}{\left( {{Y \times q_{{{Sensor}1},0}^{''}} + {{\Sigma}_{i = 1}^{m}Y \times \Delta q_{{{Sensor}1},j}^{''} \times {\psi\left( {t_{m} - t_{j - 1}} \right)}}} \right)}} & \lbrack 34\rbrack\end{matrix}$

which simplifies to:

$\begin{matrix}{T_{{Internal},m} = \frac{\begin{matrix}{{Y \times \left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right)} -} \\\left( {T_{{{Sensor}2},m} - {Y \times q_{{{Sensor}1},m}^{''} \times R_{C2}^{''}}} \right)\end{matrix}}{\left( {Y - 1} \right)}} & \lbrack 35\rbrack\end{matrix}$

Assuming negligible or equivalent thermal contact resistance (R_(C)″) ateach sensor node:

$\begin{matrix}{T_{{Internal},m} = \frac{{Y \times T_{{{Sensor}1},m}} - T_{{{Sensor}2},m}}{\left( {Y - 1} \right)}} & \lbrack 36\rbrack\end{matrix}$

In this example, Equation [35] and Equation [36] can be used forsimplified real-time internal temperature (T_(Internal,m)) measurementof a given object without any consideration for transient heat transfereffects (e.g., via a response function (ψ)) over time and/or internalparameters of the object.

Example Applications

Example embodiments are now described for different example applicationsand methods of NITI. Some of these examples have experimental dataresults included that are based on tests performed by the inventor. Thisis not meant to be an exhaustive list of applications or methods, butinstead, illustrates examples of ways NITI can be used. Furthermore,example NITI methods are not limited to the applications and/or exampleembodiments listed below and may be used and/or the basis of otherexample NITI methods for different applications and/or exampleembodiments.

The experimental data results are based on example NITI sensorembodiments that include one or more heat flux sensors based ondifferential thermopile technology and one or more temperature sensorsbased on thin-film thermocouple technology. However, similar results maybe obtained regardless of the type of heat flux sensors or temperaturesensors (e.g., RTD temperature sensors, fiber optic temperature sensors,NTC temperature sensors, thermistors, thermopiles, etc.) used.

Blood Perfusion Measurement Application

One application is Blood Perfusion (Flow) in Tissue as shown in anexample embodiment depicted in FIG. 22 . A NITI sensor (CHFT+) is shownin contact with tissue. The tissue (i.e., object) includes multipleinternal parameters including blood perfusion (w), tissue thermalconductivity (k), tissue density (ρ), and tissue heat capacity (C). Astissue depth (x) increases, the internal temperature distribution (T) ofthe tissue approaches the core blood temperature (T_(Core)). In thisexample application, the core blood temperature (T_(Core)) is assumed tobe equal to (i.e., at thermal equilibrium with) the core tissuetemperature given the majority of live tissue is composed of blood.

An example thermal mathematical model for bio-heat transfer whichincludes the effects of blood perfusion in tissue is set forth in Table2 below.

TABLE 2 Thermal Mathematical Model for Tissue with Heat Flux BoundaryCondition (based on Pennes Bio-Heat Equation) PDE$\frac{\partial T}{\partial t} = {{\alpha\frac{\partial^{2}T}{\partial x^{2}}} - {w\left( {T - T_{Core}} \right)}}$Boundary Conditions${{{- k}\frac{\partial T}{\partial x}} = {q_{Sensor}^{''}(t)}},$ x = 0 T→ T_(Core), x →∞ Initial Condition T = T_(Initial)(x), t = 0

The solution of the thermal mathematical model in Table 2 (internaltemperature distribution (T)), when evaluated at the tissue surface(x=0), is:

$\begin{matrix}{T_{{Tissue},m} = {T_{{Tissue},0} + {\sum\limits_{j = 1}^{m}{\Delta q_{{Sensor},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times Er{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 37\rbrack\end{matrix}$

where the initial tissue surface temperature is:

$\begin{matrix}{T_{{Tissue},0} = {T_{Core} + {q_{{Sensor},0}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}}}}} & \lbrack 38\rbrack\end{matrix}$

and where heat flux is defined to be positive when entering the tissue.

Rewriting Equation [37] in terms of NITI sensor outputs and includingeffects of the thermal contact resistance (R_(C)″) between the NITIsensor and the tissue surfaces yields:

$\begin{matrix}{T_{{Tissue},m} = {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}} + {\sum\limits_{j = 1}^{m}{\Delta q_{{Sensor},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times Er{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 39\rbrack\end{matrix}$${{where}\frac{1}{k}\sqrt{\frac{\alpha}{w}}} = \sqrt{\frac{1}{k\rho Cw}}$

is the steady-state thermal resistance (R″) of tissue.In this non-limiting example, the core blood temperature (T_(Core)) isassumed to be constant with time and unchanging. However, in cases wherethe core blood temperature (T_(Core)) is not constant, the effects maybe distinguished from effects related to changes in the internalparameters (e.g., blood perfusion (w)). This is due to differences inthe one or more effects resulting from such changes. For example, insome cases, effects related to changes in blood perfusion (w) can berealized via, for example, a surface temperature change that is theresult of, in this example, a non-linear expression in Equation [39].Effects related to changes in core blood temperature (T_(Core)), howevercan be realized, for example, via a surface temperature change that isthe result of, in this example, a linear expression found in acombination of Equation [38] and Equation [39]. The differences inlinear and non-linear effects allow for the distinction anddifferentiation between the different underlying causes (e.g., changesin the core blood temperature (T_(Core)) or the internal parameters).Furthermore, other thermal mathematical models may be derived to accountfor core blood temperature (T_(Core)) that varies over time as opposedto assuming core blood temperature (T_(Core)) to be constant, as in thisnon-limiting example.

Blood Perfusion—Periodic Measurements Using Parameter EstimationEmbodiment

For an example NITI sensor embodiment (e.g., CHFT+ or CHFT−) used with aperiodic data processing method, Equation [39] may be used in aparameter estimation scheme to determine the internal parameter of bloodperfusion (w), core blood (i.e., tissue) temperature (T_(Core)), and/orthe thermal contact resistance (R_(C)″) between the NITI sensor and thetissue surfaces. This is similar to the general case presented as anexample in the NITI system embodiments with one or more heat fluxsensor—temperature sensor pairs section above but with a differentthermal model for a different NITI application. In this example,predetermined constant values for the internal parameters of tissuethermal conductivity (k), tissue density (ρ), and tissue heat capacity(C) are used. An example objective function to be minimized in thisexample application is:

$\begin{matrix}{{RMSE} = \sqrt{\frac{1}{M - 1}{\sum\limits_{m = 1}^{M - 1}\left( {T_{{Sensor},m} - T_{{Calculated},m}} \right)^{2}}}} & \lbrack 40\rbrack\end{matrix}$

where:

T _(Calculated,m) =T _(Tissue,m) +q _(Sensor,m) ″×R _(C)″  [41]

and where:

$\begin{matrix}{R_{C}^{''} = \frac{{\Sigma}_{n = 1}^{N - 1}\frac{T_{{Sensor},n} - T_{{Tissue},n}}{q_{{Sensor},n}^{''}}}{N - 1}} & \lbrack 42\rbrack\end{matrix}$

An example CHFT+ embodiment (with heater) was tested on a live tissuesimulator capable of creating a controlled water perfusion andtemperature environment in pseudo tissue. This simulator is called thephantom tissue system or phantom. At different flowrates (perfusionrates), the CHFT+ was placed on the pseudo tissue and measurements weremade as follows:

-   -   10 seconds of steady-state data was recorded.    -   Heater turned on for approximately 65 seconds, resulting in a        transient thermal response of the tissue as measured by the        CHFT+ via surface heat flux and surface temperature signals.    -   The entirety of the data was processed via a periodic data        processing method that included a parameter estimation scheme in        less than 1 second, resulting in outputs of perfusion (w), core        water temperature (T_(Core)), and the thermal contact resistance        (R_(C)″) between the CHFT+ and the pseudo tissue surfaces.

TABLE 3 Results of Example Blood Perfusion CHFT+ Embodiment withPeriodic Parameter Estimation Data Processing Method${Perfusion} - {w\left( \frac{{ml}_{B/_{S}}}{{ml}_{T}} \right)}$Temperature - T_(Core) (° C.)${Flow}{Rate}\left( \frac{CC}{\min} \right)$ CHFT+ Phantom DifferenceCHFT+ Phantom $R_{C}^{''}\left( {{^\circ}{C.\frac{m^{2}}{W}}} \right)$10 0.0237 0.0185 21.94 % 32.83 32.92 0.000206 15 0.0360 0.0347 3.61 %32.12 31.93 0.000205 20 0.0533 0.0524 1.69 % 33.03 33.23 0.000254 250.0810 0.0709 12.47 % 30.24 30.48 0.000218

Looking at Table 3, the estimated values for perfusion (w) using theexample CHFT+ embodiment are in close agreement with the phantom CFDmodel (i.e., phantom) for the 15 CC/min and 20 CC/min flowrates. The 10CC/min and 25 CC/min are subject to a 21.94% and 12.47% difference,respectively. This may be because when the inventor was performing theexperimental data collection, it was difficult to maintain the 10 CC/minand 25 CC/min flowrates. When setting these flowrates, the flowratewould often skew higher than expected and resulted in higher flowmeasurements when compared against the phantom model. Note that the unitof blood perfusion (w) is denoted as ml_(B/S)/ml_(T) where a measure ofblood flow rate (e.g., milliliters of blow flow per second) through avolume of tissue (e.g. millimeter of tissue) is provided. In theseexample embodiments tested on the Phantom Tissue System, blood perfusionis instead specified as perfusion and blood flow rate is instead waterflow rate.

In some example embodiments, the unit of blood perfusion (w) may befurther reduced to s⁻¹. In other example embodiments, the unit of bloodperfusion (w) may be combined with a density value to provide a measureof blood flow rate through a given mass of tissue (e.g., 100 grams).

Furthermore, the estimated values for perfusion (w) increase as the flowrate increases. In addition, the thermal contact resistance (R_(C)″) isrelatively constant which signifies its consistency throughout theexperimental measurements, as expected. The estimated core temperatureof the perfused water (T_(Core)) matches well with the perfusing watertemperature (T_(Water)) recorded using a submerged bead thermocouplewithin the phantom. The greatest difference was about 0.24° C. occurringat 25 CC/min.

In order to demonstrate the ability of the parameter estimation schemeused in this data processing method in determining an optimal perfusion(w) value when used with experimental data, the relationship between theexample objective function in Equation [40] (i.e., RMSE) and perfusion(w) for the 15 CC/min case is displayed in FIG. 23 . The graph in FIG.23 illustrates that the relationship has a global minimum at theperfusion (w) value of 0.0360 s−1. This corresponds to the estimatedvalue of perfusion for the 15 CC/min case, as documented in Table 3.

For the 15 CC/min case, FIG. 24 is a graph illustrating an example ofmatching between a calculated (output) sensor temperature curve and ameasured (input) sensor temperature curve. The matching between the twotemperature curves indicates that the internal parameter values(k,ρ,c,w) and the thermal contact resistance (R_(C)″) value used toconstruct the calculated (output) sensor temperature curve via Equation[41] are the same as the actual values occurring in the tissue (i.e.,object). Incorrect values would result in poor matching as, for example,illustrated in FIG. 25 .

As mentioned previously, in this example, predetermined values fortissue thermal conductivity (k), tissue density (ρ), and tissue heatcapacity (c) were input as constant values in the example dataprocessing method performed for perfusion measurement above in order todetermine the internal parameter of tissue thermal inertia (√{squareroot over (kρC)}). Another way to determine tissue thermal inertia is,for example, via one or more parameter estimation schemes as a part of adata processing method.

One example way to estimate tissue thermal inertia may be to definedifferent objective functions for different time periods of surfacemeasurements made. This is possible because the calculated (output)sensor temperature curve has differing internal parameter sensitivityover time and, thus, the effects of each internal parameter (e.g.,√{square root over (kρC)} and w) can be distinguished. Consequently, theinternal parameter values can be individually estimated. FIG. 26 showsthis differing sensitivity of the calculated (output) sensor temperaturecurve to internal parameters. Specifically, there is greater sensitivityto the product of tissue thermal conductivity (k), tissue density (ρ),and tissue heat capacity (C) during the initial time period, whilesensitivity to blood perfusion (w) is initially minimal but increaseswith time. Thus, for example, in data processing methods that mayinclude parameter estimation schemes, objective functions designed todetermine an estimated value of kρC may be defined to include initialtime periods while objective functions designed to determine the valueof w may be defined to include later time periods. Additionally, theobjective functions may be defined to operate simultaneously or inprescribed sequences (e.g., one after the other).

Another example way to determine tissue thermal conductivity (k), tissuedensity (ρ), and tissue heat capacity (C) is to calculate them after ablood perfusion (w) value has been determined when using predeterminedvalues of tissue thermal conductivity (k), tissue density (ρ), andtissue heat capacity (C). For example, once an optimal blood perfusion(w) value has been determined using, for example, predetermined valuesfor the internal parameters of tissue thermal conductivity (k), tissuedensity (ρ), and tissue heat capacity (C), the quantity kρC can becalculated using, for example, Equation [43]:

$\begin{matrix}{{k\rho C} = {\frac{1}{w}\left( \frac{{\Sigma}_{j = 1}^{m}\Delta q_{{Sensor},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}{T_{{Sen{sor}},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}} - T_{{Sen{sor}},0} + {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)^{2}}} & \lbrack 43\rbrack\end{matrix}$

where the blood perfusion (w) on the right is the optimal bloodperfusion (w) value determined when using predetermined (i.e., prior)values of tissue thermal conductivity (k), tissue density (ρ), andtissue heat capacity (C).

The method based on, for example, Equation [43] can be used in a varietyof methods to determine, for example, the product of tissue thermalconductivity (k), tissue density (ρ), and tissue heat capacity (C). Forexample, measurements can be made at single or multiple indices (m). Inthe case of multiple indices, an average of the resulting values may,for example, be taken as the determined value. If desired, the morerecent determined value for kρC may update the previously determinedvalue and be used to re-estimate the blood perfusion (w) value. The morethis routine is practiced, the more accurate the determined values oftissue thermal inertia (√{square root over (kρC)}) and blood perfusion(w) may become. This non-limiting example NITI method may be used forsome or all example NITI embodiments and/or applications.

Blood Perfusion—Real-Time Measurements Using Parameter EstimationEmbodiment

In the example Blood Perfusion—Periodic Measurements using ParameterEstimation embodiment, data processing by the control circuitry startsafter all measurements are made. Thus, in the experimental phantomtesting above, measurements were output about every 75 seconds in aperiodic manner. NITI sensor (e.g., CHFT+ or CHFT−) data mayalternatively be processed in real-time to provide for real-time outputsof blood perfusion (w), core blood temperature (T_(Core)), and/orthermal contact resistance (R_(C)″) between the NITI sensor and thetissue surfaces. As time goes on, more data points are added to thesurface heat flux and surface temperature curves that are processed inreal-time by a data processing method that includes a parameterestimation scheme and outputs values in less than 1 second.

Blood Perfusion—Real-Time Measurements without Parameter EstimationEmbodiment

Equation [39] can be rearranged as:

where:

$\begin{matrix}{\sqrt{\frac{1}{k\rho cw}} = \frac{T_{{Tissue},m} - \left( {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)}{{\Sigma}_{j = 1}^{m}\Delta q_{{Sensor},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}} & \lbrack 44\rbrack\end{matrix}$T _(Tissue,m) =T _(Sensor,m) −q _(Sensor,m) ″×R _(C)″  [45]

Combining Equation [44] and Equation [45]:

$\begin{matrix}{w = \left\lbrack {k\rho{c\left( \frac{\begin{matrix}{\left( {T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}}} \right) -} \\\left( {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)\end{matrix}}{{\Sigma}_{j = 1}^{m}\Delta q_{{Sensor},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}} \right)}^{2}} \right\rbrack^{- 1}} & \lbrack 46\rbrack\end{matrix}$

When the thermal contact resistance (R_(C)″) between the NITI sensor(e.g., CHFT+ or CHFT−) and the tissue surfaces is known and typicalvalues for tissue thermal conductivity (k), tissue density (ρ), andtissue heat capacity (C) are input, Equation [46] may be used for realtime blood perfusion measurement when a typical value of blood perfusion(w) is input on the right side. In some example embodiments, for examplewhen change in blood perfusion (w) is of interest, the quantityT_(Sensor,0)−q_(Sensor,0)″×R_(C)″ may be assumed at one or morespecified times. In other example embodiments, the quantityT_(Sensor,0)−q_(Sensor,0)″×R_(C)″ may be determined by, for example,using an additional temperature sensor; the output of which isindicative of tissue surface and/or core (i.e., internal) tissuetemperature.

Although the calculated blood perfusion (w) value on the left side willnot be exact, it will still suffice for accurate quantitative and/orqualitative measurements. Furthermore, for most accurate results, thetypical value for blood perfusion (w) on the right side may be updatedto reflect the most recent and/or accurate value calculated via Equation[46]. In other methods, the values for blood perfusion (w) on the rightand left sides may be determined simultaneously, providing for accuratequantitative measurements. This may omit the need to input a typicalblood perfusion (w) value on the right side. If the thermal contactresistance (R_(C)″) value is unknown, it can be determined (e.g., viathe NITI procedures described above) or otherwise determined andaccounted for. In some cases, the thermal contact resistance (R_(C)″)may be estimated to be negligible.

Furthermore, in steady-state conditions Equation [46] reduces to:

$\begin{matrix}{w = \left\lbrack {k\rho{c\left( \frac{\begin{matrix}{\left( {T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}}} \right) -} \\\left( {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)\end{matrix}}{q_{{Sensor},m}^{''} - q_{{Sensor},0}^{''}} \right)}^{2}} \right\rbrack^{- 1}} & \lbrack 47\rbrack\end{matrix}$

Equation [47] no longer requires a typical blood perfusion (w) value onthe right side. Steady-state conditions could be achieved in a varietyof ways including a control circuitry that regulates the heat fluxand/or temperature occurring at the tissue surface via external thermaldevices (e.g., heaters, coolers, etc.).

Blood Perfusion—Duo NITI Sensor Embodiment

For an example DUO NITI sensor embodiment when using first and secondparallel NITI sensor nodes (each node having a heat fluxsensor-temperature sensor pair), two independent equations are formed:

$\begin{matrix}{{T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} = {T_{Core} + {q_{{{Sensor}1},0}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}}} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}1},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times Er{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 48\rbrack\end{matrix}$ $\begin{matrix}{{T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} = {T_{Core} + {q_{{{Sensor}2},0}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}}} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}2},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times Er{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 49\rbrack\end{matrix}$

Using an example differential based data processing method, Equation[48]-Equation [49] yields:

$\begin{matrix}{w = \left\lbrack {k\rho{c\left( \frac{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - \left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right)}{\begin{matrix}\left( {q_{{{Sensor}1},0}^{''} - q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times}} \right. \\\left. {{{Erf}\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)} - {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {{Erf}\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}} \right)\end{matrix}} \right)}^{2}} \right\rbrack^{- 1}} & \lbrack 50\rbrack\end{matrix}$

This transient equation is a result of the DUO NITI sensor configurationand allows for real time blood perfusion (w) measurement regardless ofcore blood temperature (T_(Core)), when inputting typical values fortissue thermal conductivity (k), tissue density (ρ), tissue specificheat capacity (C), and blood perfusion (w) on the right.

Although the calculated blood perfusion (w) value on the left side willnot be exact, it will still be very close and suffice for accuratequantitative and/or qualitative measurements. Furthermore, for mostaccurate results, the typical value for blood perfusion (w) may beupdated to reflect the most recent and/or accurate value calculated viaEquation [50]. In other methods, the values for blood perfusion (w) onthe right and left sides may be determined simultaneously, providing foraccurate quantitative measurements. This may omit the need to input atypical blood perfusion (w) value on the right side.

Estimated values for the thermal contact resistances (R_(C1)″ andR_(C2)″) between each NITI sensor (e.g., CHFT+ or CHFT−) and the tissuesurfaces can be determined (e.g., via NITI procedures described above)or otherwise determined. In some cases, the thermal contact resistance(R_(C1)″ and/or R_(C2)″) may be estimated to be negligible.

In steady-state conditions, Equation [50] reduces to:

$\begin{matrix}{w = \left\lbrack {k\rho{c\left( \frac{\begin{matrix}{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) -} \\\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right)\end{matrix}}{\left( {q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}} \right)} \right)}^{2}} \right\rbrack^{- 1}} & \lbrack 51\rbrack\end{matrix}$

where a typical blood perfusion (w) value is no longer required on theright side. Steady-state conditions could be achieved in a variety ofways including a control circuitry that regulates the heat flux and/ortemperature occurring at the tissue surface via external thermal devices(heaters, coolers, etc.).

FIG. 27 is a graph showing results of an example DUO CHFT+ embodimentwhen used to measure the perfusion (w) of pseudo tissue on the phantomat different flowrates of 30 CC/min, 20 CC/min and, 10 CC/min. Thisgraph shows that the example DUO CHFT+ embodiment is capable ofdetermining the perfusion (w) of pseudo tissue on the phantom wheninitially turned on at 30 CC/min (perfusion (w) rate of ˜0.035ml_(B/S)/ml_(T)). Subsequently, after about 10 minutes, the example DUOCHFT+ embodiment determines the change in perfusion (w) in real-time asthe phantom flowrate is adjusted to 10 CC/min (perfusion (w) rate of˜0.020 ml_(B/S)/ml_(T)) and later increased to 20 CC/min (perfusion (w)rate of ˜0.027 ml_(B/S)/ml_(T)), where the experimental measurements endafter about 10 minutes. To show the accuracy and agreement of theexample DUO CHFT+ method in real-time, a different example NITI methodfor perfusion measurement (CHFT+ Periodic) is also used to determine theperfusion rate at each specified flowrate. The agreement between the twomeasures indicates the validity of both methods in determining perfusion(w) rate of tissue.

Hydration of Tissue Measurement Application

All of the example methods and embodiments for Blood PerfusionMeasurement above can be also used to determine

${\sqrt{\frac{1}{k\rho{cw}}} = {\frac{1}{k}\sqrt{\frac{\alpha}{w}}}},$

which is the steady-state thermal resistance (R″) of tissue as definedin these example methods. The steady-state thermal resistance (R″) oftissue may be an accurate and reliable indicator of tissue hydration.For example, correlations could be developed and used as a means togauge tissue hydration and dehydration levels based on, for example, thetissue steady-state thermal resistance. Independent values indicative ofblood perfusion (w), or other internal parameters, may also be used togauge tissue hydration and dehydration levels.

Core Temperature of Tissue Measurement Application

Combining Equation [37] and Equation [38]:

$\begin{matrix}{T_{{Tissue},m} = {T_{Core} + {q_{{Sensor},0}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}}} + {\sum\limits_{j = 1}^{m}{\Delta q_{{Sensor},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times Er{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 52\rbrack\end{matrix}$

Rewriting Equation [52] in terms of NITI sensor outputs and includingeffects of the thermal contact resistance (R_(C)″) between the NITIsensor and the tissue surfaces:

$\begin{matrix}{{T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}}} = {T_{Core} + {q_{{Sensor},0}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}}} + {\sum\limits_{j = 1}^{m}{\Delta q_{{Sensor},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times {{Erf}\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 53\rbrack\end{matrix}$

Rearranging and realizing that T_(Core) is dependent on values thatchange over time (measurement index (m)):

$\begin{matrix}{T_{{Core},m} = {T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}} - {q_{{Sensor},0}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}}} - {\sum\limits_{j = 1}^{m}{\Delta q_{{Sensor},j}^{''} \times \frac{1}{k}\sqrt{\frac{\alpha}{w}} \times {{Erf}\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}}} & \lbrack 54\rbrack\end{matrix}$

Equation [54] is an example equation for core tissue temperature(T_(Tissue,m)) measurement and is used in the following exampleembodiments below. For some of these example embodiments, values oftissue thermal conductivity (k), tissue density (ρ), tissue specificheat capacity (C), thermal contact resistance (R_(C)″) between the NITIsensor and the tissue surfaces, and/or blood perfusion (w) need to bedetermined. This can be done by, for example, determining these values(e.g., via the CHFT+ or CHFT− methods described prior) or, for example,by using predetermined values (e.g., values from a textbook).

Core Temperature of Tissue—CHFT+ (Active Thermometry) Embodiment

A CHFT+ embodiment uses an integrated external thermal device such as aheater to create a thermal event (i.e., heat transfer) that can be usedto perform NITI. For core tissue temperature (T_(Core,m)) measurement,the heater may operate in any manner (steady, periodic, cycled, etc.)and, in this example, Equation [54] would output the core tissuetemperature (T_(Core,m)) accurately and in real-time when values forblood perfusion (w), tissue thermal conductivity (k), tissue density(ρ), tissue heat capacity (C), and estimated thermal contact resistance(R_(C)″) are input on the right side. These values could be determinedby, for example, using a data processing method (e.g., that includes aparameter estimation scheme) or otherwise determined and accounted for.In some cases, the thermal contact resistance (R_(C)″) may be estimatedto be negligible. Although not required, it may be beneficial to coverthe CHFT+ with insulating material to prevent erroneous signals fromexternal stimuli such as running, contact, etc.

FIG. 28 is a graph showing results of an example CHFT+ embodiment (withintegrated heater) when used to measure the core temperature(T_(Core,m)) of pseudo tissue on the phantom at a flowrate of 2 CC/min.In this graph, it is shown that the example CHFT+ embodiment is capableof determining the core temperature (T_(Core,m)) of pseudo tissue on thephantom (i.e., Measured (Internal)) regardless of surface temperatureconditions. Specifically, the surface temperature increases initially asa result of the integrated heater being turned on. Subsequently, after aperiod of time, the surface temperature decreases as a result of anexternal fan (i.e., thermal disturbance) being blown on the exampleCHFT+ embodiment. Regardless of these sudden and unexpected changes inthe ambient thermal conditions, the example CHFT+ embodiment measuresthe core temperature (T_(Core,m)) of the pseudo tissue with closeagreement to an internal probe placed within the phantom and under thepseudo tissue.

Core Temperature of Tissue—CHFT− (Passive Thermometry) Embodiment

A CHFT− embodiment uses external thermal events such as, for example,body heat dissipation from a mammal to perform NITI. When subject to anexternal thermal event, Equation [54], for example, would output thecore tissue temperature (T_(Core,m)), accurately and in real-time whenvalues for blood perfusion (w), tissue thermal conductivity (k), tissuedensity (ρ), tissue heat capacity (C), and estimated thermal contactresistance (R_(C)″) are input on the right side. These values could bedetermined by, for example, using a data processing method (e.g., thatincludes a parameter estimation scheme) or otherwise determined andaccounted for. In some cases, the thermal contact resistance (R_(C)″)may be estimated to be negligible. Although not required, it may bebeneficial to cover the CHFT− with insulating material to preventerroneous signals from external stimuli such as running, contact, etc.

FIG. 29 is a graph showing results of an example CHFT− embodiment whenused to measure the core temperature (T_(Core,m)) of pseudo tissue onthe phantom at a flowrate of 2 CC/min. In this graph it is shown thatthe example CHFT− embodiment is capable of determining the coretemperature (T_(Core,m)) of pseudo tissue on the phantom (i.e., Measured(Internal)) regardless of surface temperature conditions. Specifically,although the surface temperature is initially stable, an external fan(i.e., thermal disturbance) is cycled (i.e., turned on and off) to blowair on the example CHFT− embodiment and pseudo tissue. Regardless ofthese sudden and unexpected changes in the ambient thermal conditions,the example CHFT− embodiment measures the core temperature (T_(Core,m))of the pseudo tissue with close agreement to an internal probe placedwithin the phantom and under the pseudo tissue.

Core Temperature of Tissue—CHFT+(Periodic Measurement) Embodiment

In addition to the example real-time methods and embodiments for CoreTemperature of Tissue Measurement above, a NITI sensor (e.g., CHFT+ orCHFT−) can be used to make periodic measures of core tissue temperature(T_(Core)) when operating in differing steady-state conditions. Forexample, steady-state measurements prior to a thermal event(T_(Sensor,0), q_(Sensor,0)″) can be compared with steady-statemeasurements during, after, or at the end of a thermal event(T_(Sensor,END), q_(Sensor,END)″) in order to determine core tissuetemperature (T_(Core)) using:

$\begin{matrix}{T_{Core} = \frac{{T_{{Sensor},0} \times q_{{Sensor},{END}}^{''}} - {T_{{Sensor},{END}} \times q_{{Sensor},0}^{''}}}{q_{{Sensor},{END}}^{''} - q_{{Sensor},0}^{''}}} & \lbrack 55\rbrack\end{matrix}$

CHFT+ and/or CHFT− example embodiments can both be subject to differingsteady-state conditions over time. However, CHFT+ embodiments arepreferred due to the increased operational control of the one or moreexternal thermal devices that may be used to create differingsteady-state conditions.

Core Temperature—CHFT+(Zero Heat-Flux Thermometry) Embodiment

Using control circuitry, an example CHFT+ embodiment may be used tocreate a zero heat-flux environment where no heat transfer occursbetween the tissue and the sensor surfaces, i.e., where no heat entersor leaves the tissue as measured by the heat flux sensor (minimalvoltage output, i.e., “zero”). In steady-state conditions, a zeroheat-flux environment simplifies Equation [54] to:

T _(Core,m) =T _(Sensor,m)  [56]

where the measured sensor temperature (T_(Sensor,m)) is equivalent tothe core temperature of the tissue (T_(Core,m)).

An advantage of this method is the independence of core tissuetemperature (T_(Core,m)) measurement from the internal parameter values(e.g., blood perfusion (w), tissue thermal inertia (√{square root over(kρC)}′), etc.) and thermal contact resistance (R_(C)″) once asteady-state zero heat-flux environment is obtained. The amount of timerequired to achieve such steady-state conditions, as determined by themeasured sensor temperature (T_(Sensor,m)) output, varies depending onthe example embodiment used and is a common limitation of existing ZeroHeat-Flux technologies that do not utilize NITI technology. Until asteady-state zero heat-flux environment is obtained, example NITI ZeroHeat-Flux Thermometry embodiments may utilize other example embodiments,such as an example Active Thermometry embodiment for Core Temperature ofTissue Measurement, to make accurate measurements of core tissuetemperature (T_(Core,m)).

FIG. 30 is a graph showing results of an example CHFT+ Zero Heat-Flux(ZHF) embodiment when used to measure the core temperature (T_(Core,m))of pseudo tissue on the phantom at a flowrate of 2 CC/min. This graphshows that the example CHFT+ ZHF embodiment is capable of determiningthe core temperature (T_(Core,m)) of pseudo tissue on the phantomregardless of surface temperature conditions and without delay.Specifically, although the surface temperature takes approximately 8minutes to achieve an output indicative of the pseudo tissue coretemperature (T_(Core,m)), the example CHFT+ ZHF embodiment measures thecore temperature (T_(Core,m)) of the pseudo tissue from the onset withclose agreement when compared to an internal probe placed within thephantom and under the tissue.

Core Temperature—Duo NITI (Dual Thermometry) Embodiment

For an example DUO NITI embodiment when using first and second parallelNITI sensor nodes (each node having a heat flux sensor-temperaturesensor pair), two independent equations are formed:

$\begin{matrix}{{\left( {T_{{Se{nsor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{{C{ore}},m}} = {\frac{1}{k}\sqrt{\frac{\alpha}{w}}\left( {q_{{{Sensor}1},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}1},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}} \right)}} & \lbrack 57\rbrack\end{matrix}$ $\begin{matrix}{{\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) - T_{{C{ore}},m}} = {\frac{1}{k}\sqrt{\frac{\alpha}{w}}\left( {q_{{{Sensor}2},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}2},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}}} \right)}} & \lbrack 58\rbrack\end{matrix}$

Using a quotient based data processing method, Equation [57]/Equation[58] yields:

$\begin{matrix}{\frac{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{{Core},m}}{\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) - T_{{Core},m}} = \frac{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}} \right)}{\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {Er}{f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}}} \right)}} & \lbrack 59\rbrack\end{matrix}$

Rearranging:

$\begin{matrix}{T_{{Core},m} = \frac{\begin{matrix}{\left( {T_{{{Sensor}2},m} - q_{{{Sensor}2},m}^{''} + R_{C2}^{''}} \right) \times} \\\begin{matrix}{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {Er}f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}} \right) -} \\\begin{matrix}{\left( {T_{{{Sensor}1},m} - q_{{{Sensor}1},m}^{''} + R_{C1}^{''}} \right) \times} \\\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {Er}f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}} \right)\end{matrix}\end{matrix}\end{matrix}}{\begin{matrix}{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times {Er}f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}} \right) -} \\\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times {Er}f\left( \sqrt{w\left( {t_{m} - t_{j - 1}} \right)} \right)}} \right)\end{matrix}}} & \lbrack 60\rbrack\end{matrix}$

This transient equation is a result of the DUO NITI configuration andallows for real time core tissue temperature (T_(Core,m)) measurementwhen inputting typical values for tissue thermal conductivity (k),tissue density (ρ), tissue specific heat capacity (C), and bloodperfusion (w) on the right side.

Estimated values for the thermal contact resistances (R_(C1)″ andR_(C2)″) between each NITI sensor node (e.g., CHFT+ or CHFT−) and thetissue surfaces can be determined (e.g., via NITI procedures describedabove) or otherwise determined and accounted for. In some cases, thethermal contact resistances (R_(C1)″ and/or R_(C2)″) may be estimated tobe negligible.

In steady-state conditions, and where R_(C1)″≈R_(C1)″≈R_(C2)″ or R_(C1)″and R_(C2)″ are estimated to be negligible, Equation [60] reduces to:

$\begin{matrix}{T_{{Core},m} = \frac{{T_{{{Sensor}2},m} \times q_{{{Sensor}1},m}^{''}} - {T_{{{Sensor}1},m} \times q_{{{Sensor}2},m}^{''}}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 61\rbrack\end{matrix}$

where typical values for tissue thermal conductivity (k), tissue density(ρ), tissue specific heat capacity (C), and blood perfusion (w) are nolonger required on the right side. Steady-state conditions could beachieved in a variety of ways including a control circuitry thatregulates the heat flux and/or temperature occurring at the tissuesurface via external thermal devices (e.g., heaters, coolers, etc.).

Pipe Parameter Determination Application

FIG. 31 shows another application of NITI technology to determine one ormore internal parameters related to fluid flowing in a pipe or otherconduit. In this example, a heater is used (example CHFT+ embodiment),but in other examples, the heater (i.e., external thermal device) isoptional.

An example thermal mathematical solution for a pipe or other conduit(e.g., a copper pipe) with internal flow when subject to surface heatflux is:

$\begin{matrix}{T_{{Pipe},m} = {T_{{Pipe},0} + {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 62\rbrack\end{matrix}$

where the initial pipe surface temperature is:

$\begin{matrix}{T_{{Pipe},0} = {T_{Fluid} + \frac{q_{{Sensor},0}^{''}}{h}}} & \lbrack 63\rbrack\end{matrix}$

where heat flux is defined to be positive when entering the pipe/conduitand where

$\tau = \frac{\rho C\delta}{h}$

is the thermal time constant (i.e., time constant) of the pipe/conduit,ρ is the density of the pipe/conduit, C is the specific heat capacity ofthe pipe/conduit, δ is the wall thickness of the pipe/conduit, h is theinternal convection heat transfer coefficient (i.e., convectioncoefficient) of the pipe/conduit and related to the internal flowrate(i.e., flowrate) of the pipe/conduit, T_(Pipe) is the pipe/conduitsurface temperature, and T_(Fluid) is the core (i.e., internal) fluidtemperature.

Rewriting Equation [62] in terms of NITI sensor outputs and includingeffects of the thermal contact resistance (R_(C)″) between the NITIsensor and the pipe/conduit surfaces yields:

$\begin{matrix}{T_{{Pipe},m} = {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}} + {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 64\rbrack\end{matrix}$ ${where}\frac{1}{h}$

is the steady-state thermal resistance (R″) of convective internalflowrate.

Equation [62] and Equation [64] are valid for pipes or conduits made ofmaterials with high thermal conductivity. For other materials, such asPVC, a different thermal model and corresponding solution may need to bedeveloped. Other thermal models and solutions may also be developed formaterials with high thermal conductivity.

In this example, the greater the flowrate ({dot over (v)}), the greaterthe convection heat transfer coefficient (h). The relationship between1, and h is typically not linear, unless at low (e.g., laminar)flowrates, and a correlation function between the two variables istherefore desirable. This correlation function can be found, forexample, through experimental testing. One example of a correlationexperimentally found when a CHFT+ was operated on a ¾″ (0.01905 m) innerdiameter L type copper pipe with a 0.05″ (0.00127 m) wall thickness is:

$\begin{matrix}{h = {103{5.{2\left\lbrack {\frac{W}{m^{2} - {{^\circ}C}}\left( \frac{\min}{gal} \right)^{{0.2}137}} \right\rbrack}}{\overset{˙}{v}}^{0.2137}}} & \lbrack 65\rbrack\end{matrix}$

Rearranging:

$\begin{matrix}{\overset{.}{v} = {1*1{0^{{- 1}4}\left\lbrack {\frac{gal}{\min}\left( \frac{m^{2} - {{^\circ}C}}{W} \right)^{{4.6}475}} \right\rbrack}h^{{4.6}475}}} & \lbrack 66\rbrack\end{matrix}$

Thus, an example general form of a correlation between convectioncoefficient (h) and flowrate ({dot over (v)}), may be:

$\begin{matrix}{h = {{Z\left\lbrack {\frac{W}{m^{2} - {{^\circ}C}}\left( \frac{\min}{gal} \right)^{P}} \right\rbrack}{\overset{˙}{v}}^{P}}} & \lbrack 67\rbrack\end{matrix}$

where Z and P are correlation values.Other forms of correlations can be developed depending on mathematicaltechniques used (e.g., logarithmic functions, exponentials, etc.).

FIG. 32 is a graph showing how the example correlation may be developedwith experimental measurements. In this example, the correlation isfound by plotting the experimental results for measurements made atdifferent flowrates. Once a sufficient number of measurements are madeat different flowrates, a best fit curve (e.g., trend line) can be usedto find a correlation (i.e., equation) relating measured convectioncoefficient (h) to flowrate ({dot over (v)}) or vice versa.

In other example embodiments, correlations functions and/or othermethods of relating the convection heat transfer coefficient (h) to theflowrate ({dot over (v)}), or vice versa, may be determined usingmachine learning methods (e.g., neural networks, etc.).

Pipe Application—Periodic Measurements Using Parameter EstimationEmbodiment

For an example NITI sensor embodiment (e.g., CHFT+ or CHFT−) with aperiodic data processing method, Equation [64] may be used in aparameter estimation scheme to determine the internal parameter ofconvection coefficient (h), core (i.e., internal) fluid temperature(T_(Fluid)), and/or the thermal contact resistance (R_(C)″) between theNITI sensor and the pipe/conduit surfaces. This is similar to thegeneral case presented as an example for example NITI system embodimentswith one or more heat flux sensor-temperature sensor pairs section abovebut with a different thermal model for a different NITI application. Inthis example, predetermined constant values for the internal parametersof pipe density (ρ), pipe heat capacity (C), and pipe wall thickness (δ)were used. In this example, the predetermined values were obtained fromthe pipe manufacturer specification. An example objective function to beminimized in this example application is:

$\begin{matrix}{{RMSE} = \sqrt{\frac{1}{M - 1}{\sum\limits_{m = 1}^{M - 1}\left( {T_{{sensor},m} - T_{{Calculated},m}} \right)^{2}}}} & \lbrack 68\rbrack\end{matrix}$

where:

T _(Calculated,m) =T _(Pipe,m) +q _(Sensor,m) ″×R _(C)″  [69]

$\begin{matrix}{R_{C}^{''} = \frac{{\Sigma}_{n = 1}^{N - 1}\frac{T_{{Sensor},n} - T_{{Pi{pe}},n}}{q_{{sensor},n}}}{N - 1}} & \lbrack 70\rbrack\end{matrix}$

and where:

An example CHFT+ embodiment (with heater) was tested on a ¾″ (0.01905 m)inner diameter L type copper pipe with a 0.05″ (0.00127 m) wallthickness with water flowing through it at different flowrates andtemperatures. The CHFT+ was attached to the pipe surface andmeasurements were made as follows:

-   -   10 seconds of steady-state data was recorded.    -   Heater turned on for approximately 65 seconds, resulting in a        transient thermal response of the pipe wall as measured by the        CHFT+ via surface heat flux and surface temperature signals.    -   The entirety of the data was processed via a periodic data        processing method that included a parameter estimation scheme in        less than 1 second, resulting in outputs of convection        coefficient (h), core water temperature (T_(Fluid)), and thermal        contact resistance (R_(C)″) between the CHFT+ and the pipe        surfaces.

Once the convection coefficient (h) is determined, it is used in acorrelation equation (e.g., Equation [66]) to determine flowrate whichis related to fluid mass flowrate and speed (e.g., kg/s and m/s).Results are tabulated in Table 4 below.

TABLE 4 Results of Pipe Parameter Determination (Example CHFT+Embodiment with Periodic Parameter Estimation)${Flowrate}\left( \frac{gal}{\min} \right)$$h\left( \frac{W}{m^{2}{^\circ}{C.}} \right)$ τ(s)$R_{C}^{''}\left( {{^\circ}{C.\frac{m^{2}}{W}}} \right)$ RMSE (° C.)${CHFT} + {{Estimated}{Flowrate}\left( \frac{gal}{\min} \right)}$ 1 8385.22 0.000331 0.126 0.9 829 5.27 0.000327 0.134 0.9 825 5.30 0.0003340.134 0.9 826 5.29 0.000331 0.143 0.9 826 5.29 0.000334 0.137 0.9 8265.29 0.000329 0.041 0.9 4 1378 3.17 0.000329 0.041 3.9 1385 3.160.000329 0.038 4.0 1377 3.17 0.000329 0.043 3.9 1366 3.20 0.000328 0.0413.7 1388 3.15 0.000328 0.037 4.0 1401 3.12 0.000331 0.036 4.2 7 15882.75 0.000331 0.023 7.5 1585 2.76 0.000328 0.023 7.4 1583 2.76 0.0003290.024 7.4 1594 2.74 0.000328 0.021 7.6 1589 2.75 0.000331 0.022 7.5 15992.73 0.00033 0.023 7.8 10 1687 2.59 0.000332 0.020 10.0 1695 2.580.000333 0.021 10.2 1690 2.59 0.000331 0.021 10.0 1688 2.59 0.0003330.023 10.0 1683 2.60 0.000331 0.022 9.8 1682 2.60 0.000331 0.025 9.8 131786 2.45 0.000332 0.019 13.0 1796 2.43 0.000331 0.019 13.3 1808 2.420.000331 0.020 13.7 1794 2.44 0.000329 0.019 13.2 1794 2.44 0.0003290.020 13.2 1800 2.43 0.00033 0.020 13.5 16 1869 2.34 0.000329 0.019 16.01864 2.35 0.00033 0.020 15.8 1863 2.35 0.000331 0.021 15.8 1857 2.350.00033 0.020 15.6 1863 2.35 0.000331 0.025 15.8 1857 2.35 0.00033 0.02115.6

In order to demonstrate the ability of the parameter estimation schemeused in this data processing method in determining an optimal convectioncoefficient (h) value when used with experimental data, the relationshipbetween the example objective function in Equation [68] (i.e., RMSE) andconvection coefficient (h) for the 10 gal/man case is displayed in FIG.33 . The graph in FIG. 33 illustrates that the relationship has a globalminimum at the convection coefficient (h) value of 1690 w/m²C. Thiscorresponds to the estimated value for the 10 gal/min case, asdocumented in Table 4.

For the 10 gal/min case, FIG. 34 is a graph illustrating an example ofmatching between a calculated (output) sensor temperature curve and ameasured (input) sensor temperature curve. The matching between the twotemperature curves indicates that the internal parameter values (h, ρ,C, δ) and the thermal contact resistance (R_(C)″) value used toconstruct the calculated (output) sensor temperature curve via Equation[69] are the same as the actual values occurring in the pipe (i.e.,object).

As mentioned previously, in this example, predetermined values for pipedensity (ρ), pipe heat capacity (C), and pipe wall thickness (δ) weredetermined using the manufacturer's specification of the copper pipingand input as constant values in the example data processing methodperformed for pipe parameter determination. Although it was determinedas a part of the data processing method in this example, the value forthe estimated thermal contact resistance (R_(C)″) can also be input as apredetermined value beforehand and still achieve similar results. Inthis example embodiment, whether the predetermined value for the thermalcontact resistance (R_(C)″) is accurate or not, the flowrate ({dot over(v)}) results output may be accurate because the effect of anyinaccuracies in the predetermined value of the thermal contactresistance (R_(C)″) is compensated by the subsequently developedcorrelation.

Another way to define and determine the thermal contact resistance(R_(C)″) is by using the overall definition of heat transfercoefficient, U, where:

$\begin{matrix}{\frac{1}{U} = {\frac{1}{h} + R_{C}^{''}}} & \lbrack 71\rbrack\end{matrix}$

U (i.e., the total steady-state thermal resistance of the object) can bedetermined via a number of methods. One example method is to use themeasurements made in steady-state conditions (e.g., before, after, or atthe end of a thermal event) where, for example:

$\begin{matrix}{U = \frac{q_{{Sensor},{END}}^{''}}{T_{{Sensor},{END}} - T_{{Fluid},{END}}}} & \lbrack 72\rbrack\end{matrix}$

Thus, thermal contact resistance (R_(C)″) can be defined as:

$\begin{matrix}{R_{C}^{''} = {\frac{T_{{Sensor},{END}} - T_{{Fluid},{END}}}{q_{{Sensor},{END}}} - \frac{1}{h}}} & \lbrack 73\rbrack\end{matrix}$

and substituted instead of Equation [70]. In order to utilize Equation[73], the value of T_(Fluid,END) typically needs to be determined. Someexample methods of determining T_(Fluid,END) (i.e., T_(Fluid,m)) aredescribed below. In other example embodiments, T_(Fluid,m) may beassumed or otherwise determined using, for example, surface mountedtemperature sensors that may be insulated.

Another example method in determining U is to use measurements made indiffering steady-state conditions (e.g., before, at the end of, or aftera thermal event):

$\begin{matrix}{U = \frac{q_{{Sensor},{END}}^{''} - q_{{Sensor},0}^{''}}{T_{{Sensor},{END}} - T_{{Sensor},0}}} & \lbrack 74\rbrack\end{matrix}$

where q_(Sensor,END)″ and T_(Sensor,END) represent heat flux and surfacetemperature measurements made in steady-state conditions at the end of athermal event.It should be noted that Equation [74] requires differing steady-stateconditions which, for example, can be obtained by making measurementsbefore and after a thermal event is generated via, for example, anexternal thermal device.

Using Equation [74] and Equation [71]:

$\begin{matrix}{R_{C}^{''} = {\frac{T_{{Sensor},{END}} - T_{{Sensor},0}}{q_{{Sensor},{END}}^{''} - q_{{Sensor},0}^{''}} - \frac{1}{h}}} & \lbrack 75\rbrack\end{matrix}$

A data processing method that includes a parameter estimation scheme andflowrate ({dot over (v)}) correlation may also be performed withoutdifferentiating between the convection heat transfer coefficient (h) andthe thermal contact resistance (R_(C)″). Instead, the data processingmethod may be based on a thermal solution that is expressed using theoverall heat transfer coefficient (U) as, for example, illustrated inEquation [76]:

$\begin{matrix}{T_{{{Calculated}\_ U},m} = {T_{{Sensor},0} + {\sum\limits_{j = 1}^{m}{\frac{\left( {q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}} \right)}{U}\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 76\rbrack\end{matrix}$

where T_(Calculated_U,m) is the calculated (output) temperature curvefound when using the overall heat transfer coefficient (U). Furthermore,the example objective function in this example embodiment may be:

$\begin{matrix}{{RMSE} = \sqrt{\frac{1}{M - 1}{\sum\limits_{m = 1}^{M - 1}\left( {T_{{sensor},m} - T_{{{Calculated}\_ U},m}} \right)^{2}}}} & \lbrack 77\rbrack\end{matrix}$

This method is especially useful when the estimated thermal contactresistance (R_(C)″) is minimal or otherwise estimated to be negligible.

Pipe Application—Real-Time Measurements Using Parameter EstimationEmbodiment

In the example Pipe Application—Periodic Measurements using ParameterEstimation embodiment, data processing by the control circuitry startsafter all measurements are made. Thus, in the experimental pipe testingabove, measurements were output about every 75 seconds in a periodicmanner. NITI sensor (e.g., CHFT+ or CHFT−) data may alternatively beprocessed in real-time to provide for real-time outputs of convectioncoefficient (h), core fluid temperature (T_(Fluid)), and/or thermalcontact resistance (R_(C)″) between the NITI sensor and the pipe/conduitsurfaces. As time goes on, more data points are added to the surfaceheat flux and surface temperature curves that are processed in real-timeby a data processing method that includes a parameter estimation schemeand outputs values in less than 1 second.

Pipe Application—Real-Time Measurements without Parameter EstimationEmbodiment

Equation [64] can be rearranged as:

$\begin{matrix}{\frac{1}{h} = \frac{T_{{Pi{pe}},m} - \left( {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)}{{\Sigma}_{j = 1}^{m}\Delta q_{{Sensor},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} & \lbrack 78\rbrack\end{matrix}$T _(Pipe,m) =T _(Sensor,m) −q _(Sensor,m) ″×R _(C)″  [79]

Combining Equation [78] and Equation [79]:

$\begin{matrix}{h = \frac{{\Sigma}_{j = 1}^{m}\Delta q_{{Sensor},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}{\left( {T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}}} \right) - \left( {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)}} & \lbrack 80\rbrack\end{matrix}$

When the thermal contact resistance (R_(C)″) between the NITI sensor(e.g., CHFT+ or CHFT−) and the pipe/conduit surfaces is known, Equation[80] may be used for real time convection coefficient (h) measurementwhen a typical value for the thermal time constant (τ) is input on theright side. As mentioned previously, the thermal time constant (τ) is afunction of convection coefficient (h). Thus, a typical value forconvection coefficient (h) needs to be determined. In some exampleembodiments, for example when change in convection coefficient (h) is ofinterest, the quantity T_(Sensor,0)−Q_(Sensor,0)″×R_(C)″ may be assumedat one or more specified times. In other example embodiments, thequantity T_(Sensor,0)−q_(Sensor,0)″×R_(C)″ may be determined by, forexample, using an additional temperature sensor; the output of which isindicative of pipe surface and/or core (i.e., internal) fluidtemperature.

Although the calculated convection coefficient (h) value on the leftside will not be exact, it will still suffice for accurate quantitativeand/or qualitative measurements. Furthermore, for most accurate results,the typical value for convection coefficient (h), as relates to thethermal time constant (τ), on the right side may be updated over time toreflect the most recent and/or accurate value calculated via Equation[80]. In other methods, the values for convection coefficient (h) on theright and left sides may be determined simultaneously, providing foraccurate quantitative measurements. This may omit the need to input atypical convection coefficient (h) value on the right side. If thethermal contact resistance (R_(C)″) value is unknown, it can bedetermined (e.g., via the NITI procedures described above) or otherwisedetermined and accounted for. In some cases, the thermal contactresistance (R_(C)″) may be estimated to be negligible.

Inputting the determined convection coefficient (h) value from Equation[80] into a correlation equation (e.g., Equation [66]) results incorresponding flowrate ({dot over (v)}) values in real-time.

Furthermore, in steady-state conditions, Equation [80] reduces to:

$\begin{matrix}{h = \frac{q_{{Sensor},m}^{''} - q_{{Sensor},0}^{''}}{\left( {T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}}} \right) - \left( {T_{{Sensor},0} - {q_{{Sensor},0}^{''} \times R_{C}^{''}}} \right)}} & \lbrack 81\rbrack\end{matrix}$

Equation [80] no longer requires a typical thermal time constant (τ)value on the right side. Steady-state conditions could be achieved in avariety of ways including a control circuitry that regulates the heatflux and/or temperature occurring at the surface via external thermaldevices (e.g., heaters, coolers, etc.).

Similar rearrangement can be done for Equation [76] where the overallheat transfer coefficient (U) is utilized and yields:

$\begin{matrix}{U = \frac{{\Sigma}_{j = 1}^{m}\Delta q_{{Sensor},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}{T_{{Sensor},m} - T_{{Sensor},0}}} & \lbrack 82\rbrack\end{matrix}$

and in steady-state conditions:

$\begin{matrix}{U = \frac{q_{{Sensor},m}^{''} - q_{{Sensor},0}^{''}}{T_{{Sensor},m} - T_{{Sensor},0}}} & \lbrack 83\rbrack\end{matrix}$

Pipe Application—Duo NITI Sensor Embodiment

For an example DUO NITI sensor embodiment when using first and secondparallel NITI sensor nodes (each node having a heat fluxsensor-temperature sensor pair), two independent equations are formed:

$\begin{matrix}{{{T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} = {T_{Fluid} + {q_{{{Sensor}1},0}^{''} \times \frac{1}{h}} + {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}}} & \lbrack 84\rbrack\end{matrix}$ $\begin{matrix}{{T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C1}^{''}}} = {T_{Fluid} + {q_{{{Sensor}2},0}^{''} \times \frac{1}{h}} + {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 85\rbrack\end{matrix}$

Using an example differential based data processing method, Equation[84]-Equation [85] yields:

$\begin{matrix}{h = \frac{\begin{matrix}\left( {q_{{{Sensor}1},0}^{''} - q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times}} \right. \\\left. {\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right) - {{\Sigma}_{i = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right)\end{matrix}}{\begin{matrix}\left( {\left( {T_{{Se{nsor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) -} \right. \\\left. \left( {T_{{Se{nsor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) \right)\end{matrix}}} & \lbrack 86\rbrack\end{matrix}$

This transient equation is a result of the DUO NITI sensor configurationand allows for real time convection coefficient (h) measurementregardless of core fluid temperature (T_(Fluid)), when inputting atypical value for the thermal time constant (τ), a function ofconvection coefficient (h), on the right side.

Although the calculated convection coefficient (h) value on the leftside will not be exact, it will still suffice for accurate quantitativeand/or qualitative measurements. Furthermore, for most accurate results,the typical value for convection coefficient (h), as relates to thethermal time constant (τ), on the right side may be updated over time toreflect the most recent and/or accurate value calculated via Equation[86]. In other methods, the values for convection coefficient (h) on theright and left sides may be determined simultaneously, providing foraccurate quantitative measurements. This may omit the need to input atypical convection coefficient (h) value on the right side.

Estimated values for the thermal contact resistances (R_(C1)″ andR_(C2)″) between each NITI sensor node (e.g., CHFT+ or CHFT−) and thepipe/conduit surfaces can be determined (e.g., via NITI proceduresdescribed above) or otherwise determined and accounted for. In somecases, the thermal contact resistances (R_(C1)″ and/or R_(C2)″) may beestimated to be negligible.

In steady-state conditions, Equation [86] reduces to:

$\begin{matrix}{h = \frac{\left( {q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}} \right)}{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - \left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C1}^{''}}} \right)}} & \lbrack 87\rbrack\end{matrix}$

where a typical thermal time constant (τ) value is no longer required onthe right side. Steady-state conditions may be maintained in a varietyof ways including a control circuitry that regulates the heat fluxand/or temperature occurring at the surface of each sensor node viaexternal thermal devices (e.g., heaters, coolers, etc.).

An example DUO CHFT+/− embodiment with one sensor node having a heater(CHFT+) and another sensor node without a heater (CHFT−) was tested on a¾″ (0.01905 m) inner diameter L type copper pipe with a 0.05″ (0.00127m) wall thickness with water flowing through it at different flowratesand temperatures. The DUO CHFT+/− arrangement was attached to the pipesurface and measurements were compared against an example CHFT+embodiment as well as an inline flowmeter.

TABLE 5 Results of an example DUO CHFT+/−Embodiment Flowmeter CHFT+ DUOCHFT+/− ${Flowrate}\left( \frac{gal}{\min} \right)$${Flowrate}\left( \frac{gal}{\min} \right)$${Flowrate}\left( \frac{gal}{\min} \right)$ 4.0 3.8 3.9 7.0 7.3 7.5 10.09.8 10.4 13.0 13.1 12.9 16.0 15.9 15.6

Similar rearrangement can be done for Equation [76], where the overallheat transfer coefficient (U) is utilized, and yield:

$\begin{matrix}{h = \frac{\begin{matrix}\left( {q_{{{Sensor}1},0}^{''} - q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times}} \right. \\\left. {\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right) - {{\Sigma}_{i = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right)\end{matrix}}{T_{{{Sensor}1},m} - T_{{Sensor}2.m}}} & \lbrack 88\rbrack\end{matrix}$

and at steady-state:

$\begin{matrix}{U = \frac{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}{T_{{{Sensor}1},m} - T_{{{Sensor}2},m}}} & \lbrack 89\rbrack\end{matrix}$

In addition to flowrate ({dot over (v)}), and core fluid temperature(T_(Fluid)), this NITI application (i.e., Pipe Parameter Determination)may be capable of determining the thermal energy being transferred bythe flow inside of the pipe, a function of {dot over (v)} and T_(Fluid).

Corrosion/Fouling Detection Application

All of the example methods and example embodiments for Pipe ParameterDetermination above determined h or U which is then input into acorrelation function to determine flowrate (12). Monitoring the value ofh or U independently may also be used to determine the occurrence ofcorrosion or fouling of a pipe/conduit over time. This is because thevalue of h or U should be consistent for a given amount of flowrateoccurring in the pipe. As corrosion or fouling occurs, the values startto change and thus, corrosion or fouling can be detected. Monitoring thethermal time constant (τ) of a pipe/conduit made, for example, of highthermal conductivity materials also yields similar capability. Forexample, in this example application, the thermal time constant (τ) is afunction of pipe/conduit properties including density (ρ), specific heatcapacity (C), and wall thickness (δ). The values of these properties areimpacted by corrosion or fouling which consequently affect the thermaltime constant (τ) of the pipe/conduit.

Internal Temperature of Pipe or Conduit Measurement Application

Combining Equation [62] and Equation [63]:

$\begin{matrix}{T_{{Pipe},m} = {T_{Fluid} + \frac{q_{{Sensor},0}^{''}}{h} + {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 90\rbrack\end{matrix}$

Rewriting Equation [90] in terms of NITI sensor outputs and includingeffects of the thermal contact resistance (R_(C)″) between the NITIsensor and the pipe/conduit surfaces:

$\begin{matrix}{{T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}}} = {T_{Fluid} + \frac{q_{{Sensor},0}^{''}}{h} + {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 91\rbrack\end{matrix}$

Rearranging and realizing that T_(Fluid) is dependent on values thatchange over time (measurement index (m)):

$\begin{matrix}{T_{{Fluid},m} = {T_{{Sensor},m} - {q_{{Sensor},m}^{''} \times R_{C}^{''}} - \frac{q_{{Sensor},0}^{''}}{h} - {\sum\limits_{j = 1}^{m}{\left( \frac{q_{{Sensor},j}^{''} - q_{{Sensor},{j - 1}}^{''}}{h} \right)\left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}}} & \lbrack 92\rbrack\end{matrix}$

Equation [92] is an example equation for core fluid temperature(T_(Fluid,m)) measurement in pipes or conduits with high thermalconductivity (e.g., copper) and is used in the following exampleembodiments below. For some of these example embodiments, values ofconvection coefficient (h), estimated thermal contact resistance(R_(C)″) between the NITI sensor and the pipe/conduit surfaces, and/orthermal time constant (τ) need to be determined. This can be done by,for example, determining these values (e.g., via the CHFT+ or CHFT−methods described prior) or by inputting predetermined values (e.g.,values from a textbook).

Similar example embodiments to those below can be used with Equation[76], where the overall heat transfer coefficient (U) is utilizedinstead of a combination of convection coefficient (h) and thermalcontact resistance (R_(C)″) between the NITI sensor and the pipe/conduitsurfaces.

Pipe Internal Temperature—CHFT+(Active Thermometry) Embodiment

A CHFT+ embodiment uses an integrated external thermal device such as aheater to create a thermal event (i.e., heat transfer) that can be usedto perform NITI. For core fluid temperature (T_(Fluid,m)) measurement,the heater may operate in any manner (steady, periodic, cycled, etc.)and, in this example, Equation [92] would output the core fluidtemperature (T_(Fluid,m)) accurately and in real-time when values forconvection coefficient (h), thermal time constant (τ), and estimatedthermal contact resistance (R_(C)″) are input on the right side. Thesevalues could be determined by, for example, using a data processingmethod (e.g., that includes a parameter estimation scheme) or otherwisedetermined and accounted for. In some cases, the thermal contactresistance (R_(C)″) may be estimated to be negligible. Although notrequired, it may be beneficial to cover the CHFT+ with insulatingmaterial to prevent erroneous signals from external stimuli such asambient changes, contact, etc.

Table 6 provides experimental results from an example CHFT+ embodiment(with integrated heater) when used to measure the core fluid temperature(T_(Fluid,m)) of a ¾″ (0.01905 m) inner diameter L type copper pipe witha 0.05″ (0.00127 m) wall thickness at different flowrates where themeasurements of core fluid temperature measurement (T_(Fluid,m)) havebeen averaged over time:

TABLE 6 Example CHFT+ Embodiment Results for Internal Pipe Temperature${Flowrate}\left( \frac{gal}{\min} \right)$ CHFT+ Output (° C.)T_(Fluid) Measured (° C.) |ΔT| (° C.) 1 24.76 24.86 0.10 24.98 25.090.11 25.18 25.30 0.12 25.42 25.52 0.10 25.62 25.73 0.11 25.85 25.95 0.104 22.28 22.41 0.13 22.45 22.58 0.13 22.75 22.86 0.11 22.95 23.10 0.1523.25 23.31 0.06 23.70 23.84 0.14 7 22.65 22.68 0.03 22.86 22.91 0.0523.14 23.19 0.05 23.40 23.46 0.06 23.77 23.85 0.08 24.12 24.17 0.05 1025.46 25.58 0.12 25.66 25.76 0.10 29.24 29.27 0.03 29.63 29.69 0.0629.89 29.86 0.03 30.34 30.32 0.02 13 25.47 25.61 0.14 25.65 25.77 0.1225.86 25.99 0.13 26.04 26.13 0.09 26.25 26.40 0.15 26.51 26.66 0.15 1626.24 26.42 0.18 26.38 26.49 0.11 26.51 26.60 0.09 26.68 26.79 0.1126.83 27.01 0.18 27.02 27.19 0.17

FIG. 354 is a graph showing results of an example CHFT+ embodiment (withintegrated and controlled heater) when used to measure the core fluidtemperature (T_(Fluid,m)) of a ¾″ (0.01905 m) inner diameter L typecopper pipe with a 0.05″ (0.00127 m) wall thickness undergoing fluidflow at 15 gal/min. In this graph it is shown that the example CHFT+embodiment is capable of determining the core fluid temperature(T_(Fluid,m)) of a pipe regardless of surface temperature conditions.Specifically, in this example, the surface temperature increases withtime as a result of the integrated heater being turned on. Regardless ofthis consistent increase in surface temperature over time, the exampleCHFT+ embodiment measures the core fluid temperature (T_(Fluid,m))within the copper pipe with close agreement to an internal probe placedinside the pipe and within the pipe flow.

Pipe Internal Temperature—CHFT− (Passive Thermometry) Embodiment

A CHFT− embodiment uses external thermal events such as pipe heatdissipation to the environment to perform NITI. When subject to anexternal thermal event, Equation [92], for example, would output thecore fluid temperature (T_(Fluid,m)) accurately and in real-time whenvalues for convection coefficient (h), thermal time constant (τ), andestimated thermal contact resistance (R_(C)″) are input on the rightside. These values could be determined by, for example, using a dataprocessing method (e.g., that includes a parameter estimation scheme) orotherwise determined and accounted for. In some cases, the thermalcontact resistance (R_(C)″) may be estimated to be negligible. Althoughnot required, it may be beneficial to cover the CHFT− with insulatingmaterial to prevent erroneous signals from external stimuli such asambient changes, contact, etc.

Pipe Internal Temperature—CHFT+ (Periodic Measurement) Embodiment

In addition to the example real-time methods and example embodiments forInternal Temperature of Pipe or Conduit Measurement above, a NITI sensorcan be used to make periodic measures of core fluid temperature(T_(Fluid)) when operating in differing steady-state conditions. Forexample, steady-state measurements prior to a thermal event(T_(Sensor,0), q_(Sensor,0)″) can be compared with steady-statemeasurements during, after, or at the end of a thermal event(T_(Sensor,END), q_(Sensor,END)″) in order to determine core fluidtemperature (T_(Fluid)) using:

$\begin{matrix}{T_{Fluid} = \frac{{T_{{Sensor},0} \times q_{{Sensor},{END}}^{''}} - {T_{{Sensor},{END}} \times q_{{Sensor},0}^{''}}}{q_{{Sensor},{END}}^{''} - q_{{Sensor},0}^{''}}} & \lbrack 93\rbrack\end{matrix}$

CHFT+ and/or CHFT− example embodiments can both be subject to differingsteady-state conditions over time. However, CHFT+ example embodimentsare preferred due to the increased operational control of the one ormore thermal event devices that may be used to create differingsteady-state conditions.

Pipe Internal Temperature—CHFT+(Zero Heat-Flux Thermometry) Embodiment

Using control circuitry, an example CHFT+ embodiment may be used tocreate a zero heat-flux environment where no heat transfer occursbetween the pipe and the sensor surfaces, i.e., where no heat enters orleaves the pipe as measured by the heat flux sensor (minimal voltageoutput, i.e., “zero”).

In steady-state conditions, a zero heat-flux environment simplifiesEquation [92] to:

T _(Fluid,m) =T _(Sensor,m)  [94]

where the measured sensor temperature (T_(Sensor,m)) is equivalent tothe core fluid temperature (T_(Fluid,m)). The advantage of this methodis the independence of core fluid temperature (T_(Fluid,m)) measurementfrom the internal parameter values (e.g., convection coefficient (h),thermal time constant (τ), etc.) and thermal contact resistance (R_(C)″)once a steady-state zero heat-flux environment is obtained. Until asteady-state zero heat-flux environment is obtained, other embodiments,such as the Active Thermometry embodiment for Internal Temperature ofPipe or Conduit Measurement, can be utilized to make accuratemeasurements of core fluid temperature (T_(Fluid,m)). The amount of timerequired to achieve such steady-state conditions, as determined by themeasured sensor temperature (T_(Sensor,m)) output, varies depending onthe example embodiment used and is a common limitation of existing ZeroHeat-Flux technologies that do not utilize NITI technology. Until asteady-state zero heat-flux environment is obtained, example ZeroHeat-Flux Thermometry embodiments may utilize other example NITIembodiments, such as an example Active Thermometry embodiment for PipeInternal Temperature Measurement, to make accurate measurements of corefluid temperature (T_(Fluid,m)).

Pipe Internal Temperature—Duo NITI (Dual Thermometry) Embodiment

For an example DUO NITI sensor embodiment when using first and secondparallel NITI sensor nodes (each node having a heat fluxsensor-temperature sensor pair), two independent equations are formedwhen placed on a pipe/conduit made of material with high thermalconductivity:

$\begin{matrix}{{\left( {T_{{Se{nsor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{{Fl{uid}},m}} = {\frac{1}{h}\left( {q_{{{Sensor}1},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}1},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}} \right)}} & \lbrack 95\rbrack\end{matrix}$ $\begin{matrix}{{\left( {T_{{S{ensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) - T_{{Fl{uid}},m}} = {\frac{1}{h}\left( {q_{{{Sensor}2},0}^{''} + {\sum\limits_{j = 1}^{m}{\Delta q_{{{Sensor}1},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}}} \right)}} & \lbrack 96\rbrack\end{matrix}$

Using a quotient based data processing method, Equation [95]/Equation[96] yields:

$\begin{matrix}{\frac{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) - T_{{Fluid} \cdot m}}{\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times R_{C2}^{''}}} \right) - T_{{Fluid} \cdot m}} = \frac{\left( {q_{{{Sensor}1},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right)}{\left( {q_{{{Sensor}2},0}^{''} + {{\Sigma}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right)}} & \lbrack 97\rbrack\end{matrix}$

Rearranging:

$\begin{matrix}{T_{{Fluid} \cdot m} = \frac{\begin{matrix}\left( {T_{{{Sensor}2},m} - {q_{{{Sensor}2},m}^{''} \times \left( R_{C2}^{''} \right) \times}} \right. \\\begin{matrix}{\left( {q_{{{Sensor}1},0}^{''} + {{\sum}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right) -} \\\begin{matrix}{\left( {T_{{{Sensor}1},m} - {q_{{{Sensor}1},m}^{''} \times R_{C1}^{''}}} \right) \times} \\\left( {q_{{{Sensor}2},0}^{''} + {{\sum}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right)\end{matrix}\end{matrix}\end{matrix}}{\begin{matrix}{\left( {q_{{{Sensor}1},0}^{''} + {{\sum}_{j = 1}^{m}\Delta q_{{{Sensor}1},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right) -} \\\left( {q_{{{Sensor}2},0}^{''} + {{\sum}_{j = 1}^{m}\Delta q_{{{Sensor}2},j}^{''} \times \left( {1 - e^{- {(\frac{t_{m} - t_{j - 1}}{\tau})}}} \right)}} \right)\end{matrix}}} & \lbrack 98\rbrack\end{matrix}$

This transient equation is a result of the DUO NITI configuration andallows for real time core fluid temperature (T_(Fluid,m)) measurementwhen inputting typical values for convection coefficient (h) and thermaltime constant (τ) on the right side.

Estimated values for the thermal contact resistances (R_(C1)″ andR_(C2)″) between each NITI sensor node (e.g., CHFT+ or CHFT−) and thepipe/conduit surfaces can be determined (e.g., via NITI proceduresdescribed above) or otherwise determined and accounted for. In somecases, the thermal contact resistances (R_(C1)″ and/or R_(C2)″) may beestimated to be negligible.

In steady-state conditions, and where R_(C1)″≈R_(C1)″≈R_(C2)″ or R_(C1)″and R_(C2)″ are estimated to be negligible, Equation [98] reduces to:

$\begin{matrix}{T_{{Fluid} \cdot m} = \frac{{T_{{{Sensor}2},m} \times q_{{{Sensor}1},m}^{''}} - {T_{{{Sensor}1},m} \times q_{{{Sensor}2},m}^{''}}}{q_{{{Sensor}1},m}^{''} - q_{{{Sensor}2},m}^{''}}} & \lbrack 99\rbrack\end{matrix}$

where typical values for convection coefficient (h) and thermal timeconstant (τ) are no longer required on the right side. This impliesthat, when in steady-state conditions, Equation [99] can be used forpipes or conduits regardless of the pipe/conduit material, wallthickness, etc. Steady-state conditions could be achieved in a varietyof ways including a control circuitry that regulates the heat fluxand/or temperature occurring at the tissue surface via external thermaldevices (e.g., heaters, coolers, etc.).

FIG. 36 is a graph showing results of an example DUO CHFT+/− embodiment(one sensor node with heater and one sensor node without) when used tomeasure the internal temperature of a ¾″ (0.01905 m) inner diameter Ltype copper pipe with a 0.05″ (0.00127 m) wall thickness undergoingfluid flow at 15 gal/min. In this example, both sensor nodes werecovered with insulation in order to prevent sporadic heat transfer andtemperature signals from impacting the quality of measurement. Thisexample was conducted in both steady-state and transient conditions. Asshown in the graph, there is close agreement between the example DUOCHFT+/− embodiment and an internal probe (placed inside the pipe andwithin the pipe flow).

FIG. 37 is a graph showing results of an example DUO CHFT+/− embodiment(one sensor node with heater and one sensor node without) when used tomeasure the internal temperature of a 1.939″ (0.0492506 m) innerdiameter Schedule 80 CPVC pipe with a 0.218″ (0.0055372 m) wallthickness undergoing fluid flow at 50 gal/min. In min this example, bothsensor nodes were not covered with insulation. This example wasconducted in steady-state conditions where the internal parameters ofthe pipe are not required to make accurate measurements. As shown in thegraph, there is close agreement between the example DUO CHFT+/−embodiment and an internal probe (placed inside the pipe and within thepipe flow). There are, however, more sporadic measurements as a resultof not covering the sensors nodes with insulation.

Although various example embodiments have been shown and described indetail, the claims are not limited to any particular embodiment orexample. Moreover, example embodiments above use thermal signals (e.g.,heat transfer and temperature signals) combined with analyticalsolutions that are based on thermal mathematical models to determine oneor more internal properties of an object. Other example embodiments mayutilize other methods including, but not limited to, empirical methods,machine learning methods (e.g., neural networks), regression basedmethods, artificial intelligence based methods, moving average basedmethods, etc. in order to determine one or more internal properties ofan object based on thermal signals measured at the object surface.

In other example embodiments, the output of other non-NITI based devicesmay be used in conjunction with NITI techniques to determine one or moreinternal properties of the internal region of an object. For example,the output of an internal temperature probe within a pipe may be usedwith a surface mounted NITI sensor to determine flowrate within thepipe.

In the present application, the words “configured to . . . ” are used tomean that an element of an apparatus has a configuration able to carryout the defined operation. A “configuration” may also refer to anarrangement or manner of interconnection of hardware or software. Forexample, the apparatus may have dedicated hardware which provides thedefined operation, or a processor or other processing device may beprogrammed to perform the function. “Configured to” does not imply thatthe apparatus element needs to be changed in any way in order to providethe defined operation.

None of the above description should be read as implying that anyparticular member, step, range, or function is essential. All structuraland functional equivalents to the members of the above-describedembodiments that are known to those of ordinary skill in the art areincorporated herein by reference and are intended to be encompassed.Furthermore, no embodiment, feature, component, or step in thisspecification is intended to be dedicated to the public.

Although illustrative embodiments have been described in detail hereinwith reference to the accompanying drawings, it is to be understood thatthe invention is not limited to those precise embodiments, and thatvarious changes and modifications can be effected therein by one skilledin the art without departing from the scope of the appended claims.

1. A system for non-invasive sensing of an object having a volume with a surface and an internal region, comprising: a non-invasive sensor including: a heat flux sensor having one or more heat flux sensor output terminals; a temperature sensor having one or more temperature sensor output terminals, wherein the non-invasive sensor is adapted to be placed on or near the surface of the object, where the internal region of the object has internal properties indicated by one or more corresponding internal parameters and an internal temperature distribution, and circuitry coupled to the one or more heat flux sensor output terminals and the one or more temperature sensor output terminals to: receive a measured temperature signal from the temperature sensor at one or more specified times; receive a measured heat flux signal from the heat flux sensor at one or more specified times; determine an estimated indicative quantity for one or more of the internal properties at one or more specified times based on at least the measured temperature signal and the measured heat flux signal; and generate information indicating one or more of the one or more estimated indicative quantities determined for the one or more internal properties at one or more specified times.
 2. The system of claim 1, wherein the non-invasive sensor is subject to differing steady-state conditions.
 3. The system of claim 1, wherein the one or more heat flux sensor output terminals and the one or more temperature sensor output terminals are coupled to interconnected circuitry. 